2000 character limit reached
Ground state energy of dilute Bose gases in 1D
Published 31 Mar 2022 in math-ph, math.MP, and quant-ph | (2203.17183v3)
Abstract: We study the ground state energy of a gas of 1D bosons with density $\rho$, interacting through a general, repulsive 2-body potential with scattering length $a$, in the dilute limit $\rho |a|\ll1$. The first terms in the expansion of the thermodynamic energy density are $\pi2\rho3/3(1+2\rho a)$, where the leading order is the 1D free Fermi gas. This result covers the Tonks-Girardeau limit of the Lieb-Liniger model as a special case, but given the possibility that $a>0$, it also applies to potentials that differ significantly from a delta function. We include extensions to spinless fermions and 1D anyonic symmetries, and discuss an application to confined 3D gases.
- Lee, T.D., Huang, K., Yang, C.N.: Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties. Physical Review 106(6), 1135 (1957) Dyson [1957] Dyson, F.J.: Ground-state energy of a hard-sphere gas. Physical Review 106(1), 20 (1957) Lieb and Yngvason [1998] Lieb, E.H., Yngvason, J.: Ground state energy of the low density Bose gas. In: The Stability of Matter: From Atoms to Stars, pp. 755–758. Springer, ??? (1998) Yau and Yin [2009] Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dyson, F.J.: Ground-state energy of a hard-sphere gas. Physical Review 106(1), 20 (1957) Lieb and Yngvason [1998] Lieb, E.H., Yngvason, J.: Ground state energy of the low density Bose gas. In: The Stability of Matter: From Atoms to Stars, pp. 755–758. Springer, ??? (1998) Yau and Yin [2009] Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: Ground state energy of the low density Bose gas. In: The Stability of Matter: From Atoms to Stars, pp. 755–758. Springer, ??? (1998) Yau and Yin [2009] Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. 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[2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? 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Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: Ground state energy of the low density Bose gas. In: The Stability of Matter: From Atoms to Stars, pp. 755–758. Springer, ??? (1998) Yau and Yin [2009] Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Lieb, E.H., Yngvason, J.: Ground state energy of the low density Bose gas. In: The Stability of Matter: From Atoms to Stars, pp. 755–758. Springer, ??? (1998) Yau and Yin [2009] Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Yau, H.-T., Yin, J.: The second order upper bound for the ground energy of a Bose gas. Journal of Statistical Physics 136(3), 453–503 (2009) Fournais and Solovej [2020] Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute Bose gases. Annals of Mathematics 192(3), 893–976 (2020) Basti et al. [2021] Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. 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[2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? 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[2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Basti, G., Cenatiempo, S., Schlein, B.: A new second-order upper bound for the ground state energy of dilute Bose gases. In: Forum of Mathematics, Sigma, vol. 9 (2021). Cambridge University Press Fournais and Solovej [2023] Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Solovej, J.P.: The energy of dilute bose gases ii: The general case. Inventiones mathematicae 232(2), 863–994 (2023) Schick [1971] Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. 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Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. 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Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? 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Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Schick, M.: Two-dimensional system of hard-core bosons. Physical Review A 3(3), 1067 (1971) Lieb and Yngvason [2001] Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Yngvason, J.: The ground state energy of a dilute two-dimensional Bose gas. Journal of Statistical Physics 103(3), 509–526 (2001) Andersen [2002] Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. 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[2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Andersen, J.O.: Ground state pressure and energy density of an interacting homogeneous Bose gas in two dimensions. The European Physical Journal B-Condensed Matter and Complex Systems 28(4), 389–396 (2002) Mora and Castin [2009] Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. 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[2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? 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Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Mora, C., Castin, Y.: Ground state energy of the two-dimensional weakly interacting Bose gas: first correction beyond Bogoliubov theory. Physical Review Letters 102(18), 180404 (2009) Fournais et al. [2019] Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Napiórkowski, M., Reuvers, R., Solovej, J.P.: Ground state energy of a dilute two-dimensional Bose gas from the bogoliubov free energy functional. Journal of Mathematical Physics 60(7), 071903 (2019) Fournais et al. [2022] Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Fournais, S., Girardot, T., Junge, L., Morin, L., Olivieri, M.: The ground state energy of a two-dimensional bose gas. arXiv preprint arXiv:2206.11100 (2022) Astrakharchik et al. [2010] Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Astrakharchik, G., Boronat, J., Kurbakov, I., Lozovik, Y.E., Mazzanti, F.: Low-dimensional weakly interacting bose gases: Nonuniversal equations of state. Physical Review A 81(1), 013612 (2010) Lieb and Liniger [1963] Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Liniger, W.: Exact analysis of an interacting bose gas. i. the general solution and the ground state. Physical Review 130(4), 1605 (1963) Guan and Batchelor [2011] Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Batchelor, M.T.: Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems. Journal of Physics A: Mathematical and Theoretical 44(10), 102001 (2011) Jiang et al. [2015] Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Jiang, Y.-Z., Chen, Y.-Y., Guan, X.-W.: Understanding many-body physics in one dimension from the Lieb–Liniger model. Chinese Physics B 24(5), 050311 (2015) Girardeau [1960] Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Girardeau, M.: Relationship between systems of impenetrable bosons and fermions in one dimension. Journal of Mathematical Physics 1(6), 516–523 (1960) Bogoliubov [1947] Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Bogoliubov, N.N.: On the theory of superfluidity. Proc. Inst. Math. Kyiv 9, 89–103 (1947). Rus. Trans Izv. Akad. Nauk Ser. Fiz. 11, 77 (1947), Eng. Trans. J. Phys. (USSR), 11, 23 (1947) Lieb et al. [2004] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional behavior of dilute, trapped Bose gases. Communications in mathematical physics 244(2), 347–393 (2004) Lieb and Mattis [1962] Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Lieb, E., Mattis, D.: Theory of ferromagnetism and the ordering of electronic energy levels. Physical Review 125(1), 164–172 (1962) Yang [1967] Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Yang, C.-N.: Some exact results for the many-body problem in one dimension with repulsive delta-function interaction. Physical Review Letters 19(23), 1312 (1967) Gaudin [1967] Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Gaudin, M.: Un systeme a une dimension de fermions en interaction. Physics Letters A 24(1), 55–56 (1967) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Girardeau [2006] Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Girardeau, M.: Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model. Physical Review Letters 97(21), 210401 (2006) Sutherland [1968] Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Sutherland, B.: Further results for the many-body problem in one dimension. Physical Review Letters 20(3), 98 (1968) Guan et al. [2012] Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Guan, X.-W., Ma, Z.-Q., Wilson, B.: One-dimensional multicomponent fermions with δ𝛿\deltaitalic_δ-function interaction in strong-and weak-coupling limits: κ𝜅\kappaitalic_κ-component fermi gas. Physical Review A 85(3), 033633 (2012) Leinaas and Myrheim [1977] Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Leinaas, J.M., Myrheim, J.: On the theory of identical particles. Il Nuovo Cimento B (1971-1996) 37(1), 1–23 (1977) Kundu [1999] Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Kundu, A.: Exact solution of double δ𝛿\deltaitalic_δ function bose gas through an interacting anyon gas. Physical Review Letters 83(7), 1275 (1999) Posske et al. [2017] Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Posske, T., Trauzettel, B., Thorwart, M.: Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the lieb-liniger model. Physical Review B 96(19), 195422 (2017) Bonkhoff et al. [2021] Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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[2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Bonkhoff, M., Jägering, K., Eggert, S., Pelster, A., Thorwart, M., Posske, T.: Bosonic continuum theory of one-dimensional lattice anyons. Physical Review Letters 126(16), 163201 (2021) Batchelor et al. [2006] Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Batchelor, M.T., Guan, X.-W., Oelkers, N.: One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics. Physical Review Letters 96(21), 210402 (2006) Hao et al. [2008] Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Hao, Y., Zhang, Y., Chen, S.: Ground-state properties of one-dimensional anyon gases. Physical Review A 78(2), 023631 (2008) Olshanii [1998] Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Olshanii, M.: Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Physical Review Letters 81(5), 938 (1998) Lieb et al. [2003] Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Lieb, E.H., Seiringer, R., Yngvason, J.: One-dimensional bosons in three-dimensional traps. Physical Review Letters 91(15), 150401 (2003) Seiringer and Yin [2008] Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Seiringer, R., Yin, J.: The Lieb-Liniger model as a limit of dilute bosons in three dimensions. Communications in mathematical physics 284(2), 459–479 (2008) Calabrese and Caux [2007] Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Calabrese, P., Caux, J.-S.: Correlation functions of the one-dimensional attractive Bose gas. Physical Review Letters 98(15), 150403 (2007) McGuire [1964] McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- McGuire, J.B.: Study of exactly soluble one-dimensional N𝑁Nitalic_N-body problems. Journal of Mathematical Physics 5(5), 622–636 (1964) Schreck et al. [2001] Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Schreck, F., Khaykovich, L., Corwin, K., Ferrari, G., Bourdel, T., Cubizolles, J., Salomon, C.: Quasipure bose-einstein condensate immersed in a Fermi sea. Physical Review Letters 87(8), 080403 (2001) Görlitz et al. [2001] Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Görlitz, A., Vogels, J., Leanhardt, A., Raman, C., Gustavson, T., Abo-Shaeer, J., Chikkatur, A., Gupta, S., Inouye, S., Rosenband, T., et al.: Realization of Bose-Einstein condensates in lower dimensions. Physical Review Letters 87(13), 130402 (2001) Greiner et al. [2001] Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Greiner, M., Bloch, I., Mandel, O., Hänsch, T.W., Esslinger, T.: Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Physical Review Letters 87(16), 160405 (2001) Moritz et al. [2003] Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Moritz, H., Stöferle, T., Köhl, M., Esslinger, T.: Exciting collective oscillations in a trapped 1D gas. Physical Review Letters 91(25), 250402 (2003) Bloch et al. [2008] Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Bloch, I., Dalibard, J., Zwerger, W.: Many-body physics with ultracold gases. Reviews of modern physics 80(3), 885 (2008) Lenard [1964] Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Lenard, A.: Momentum distribution in the ground state of the one-dimensional system of impenetrable bosons. Journal of Mathematical Physics 5(7), 930–943 (1964) Vaidya and Tracy [1979] Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Vaidya, H.G., Tracy, C.: One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature. Journal of Mathematical Physics 20(11), 2291–2312 (1979) Colcelli et al. [2018] Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Colcelli, A., Mussardo, G., Trombettoni, A.: Deviations from off-diagonal long-range order in one-dimensional quantum systems. EPL (Europhysics Letters) 122(5), 50006 (2018) De Rosi et al. [2019] De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- De Rosi, G., Massignan, P., Lewenstein, M., Astrakharchik, G.E.: Beyond-luttinger-liquid thermodynamics of a one-dimensional bose gas with repulsive contact interactions. Physical Review Research 1(3), 033083 (2019) Yang and Yang [1969] Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Yang, C.-N., Yang, C.P.: Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction. Journal of Mathematical Physics 10(7), 1115–1122 (1969) Dorlas [1993] Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Dorlas, T.C.: Orthogonality and completeness of the Bethe ansatz eigenstates of the nonlinear Schroedinger model. Communications in Mathematical Physics 154(2), 347–376 (1993) https://doi.org/cmp/1104252974 Robinson [1971] Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
- Robinson, D.W.: The Thermodynamic Pressure in Quantum Statistical Mechanics. Lecture Notes in Physics. Springer, ??? (1971). https://books.google.dk/books?id=IfHuoAEACAAJ
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