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Local and nonlocal electronic correlations at the metal-insulator transition in the Hubbard model in two dimensions

Published 5 Dec 2023 in cond-mat.str-el | (2312.03123v1)

Abstract: Elucidating the physics of the single-orbital Hubbard model in its intermediate coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent non-perturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong-coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.

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References (67)
  1. J. C. Slater, “Magnetic Effects and the Hartree-Fock Equation,” Phys. Rev. 82, 538 (1951).
  2. N. F. Mott, Metal-insulator transitions (London: Taylor & Francis, 1974).
  3. G. Rohringer and A. Toschi, “Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study,” Phys. Rev. B 94, 125144 (2016).
  4. Masatoshi Imada, Atsushi Fujimori,  and Yoshinori Tokura, “Metal-insulator transitions,” Rev. Mod. Phys. 70, 1039–1263 (1998).
  5. P. W. Anderson, “New approach to the theory of superexchange interactions,” Phys. Rev. 115, 2–13 (1959).
  6. K. A. Chao, J. Spałek,  and Oleś A. M., “Degenerate perturbation theory and its application to the Hubbard model,” Physics Letters A 64, 163 – 166 (1977a).
  7. K. A. Chao, J. Spałek,  and A. M. Oleś, “Kinetic exchange interaction in a narrow S-band,” Journal of Physics C: Solid State Physics 10, L271–L276 (1977b).
  8. A. H. MacDonald, S. M. Girvin,  and D. Yoshioka, “tU𝑡𝑈\frac{t}{U}divide start_ARG italic_t end_ARG start_ARG italic_U end_ARG expansion for the Hubbard model,” Phys. Rev. B 37, 9753–9756 (1988).
  9. J. Spałek, “t-J Model Then and Now: a Personal Perspective from the Pioneering Times,” Acta Physica Polonica A 111, 409–424 (2007).
  10. Antoine Georges, Gabriel Kotliar, Werner Krauth,  and Marcelo J. Rozenberg, “Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions,” Rev. Mod. Phys. 68, 13–125 (1996).
  11. M. H. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke,  and H. R. Krishnamurthy, “Nonlocal dynamical correlations of strongly interacting electron systems,” Phys. Rev. B 58, R7475–R7479 (1998).
  12. A. I. Lichtenstein and M. I. Katsnelson, “Antiferromagnetism and d-wave superconductivity in cuprates: A cluster dynamical mean-field theory,” Phys. Rev. B 62, R9283–R9286 (2000).
  13. Gabriel Kotliar, Sergej Y. Savrasov, Gunnar Pálsson,  and Giulio Biroli, “Cellular dynamical mean field approach to strongly correlated systems,” Phys. Rev. Lett. 87, 186401 (2001).
  14. Thomas A. Maier, Mark Jarrell, Thomas Pruschke,  and Matthias Hettler, “Quantum cluster theories,” Rev. Mod. Phys. 77, 1027–1080 (2005).
  15. A.-M. S. Tremblay, B. Kyung,  and D. Sénéchal, “Pseudogap and high-temperature superconductivity from weak to strong coupling. Towards a quantitative theory (Review Article),” Low Temp. Phys. 32, 424–451 (2006).
  16. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet,  and C. A. Marianetti, “Electronic structure calculations with dynamical mean-field theory,” Rev. Mod. Phys. 78, 865–951 (2006).
  17. H. Park, K. Haule,  and G. Kotliar, “Cluster dynamical mean field theory of the mott transition,” Phys. Rev. Lett. 101, 186403 (2008).
  18. Malte Harland, Mikhail I. Katsnelson,  and Alexander I. Lichtenstein, “Plaquette valence bond theory of high-temperature superconductivity,” Phys. Rev. B 94, 125133 (2016).
  19. L. Fratino, P. Sémon, M. Charlebois, G. Sordi,  and A.-M. S. Tremblay, “Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model,” Phys. Rev. B 95, 235109 (2017).
  20. G. Rohringer, H. Hafermann, A. Toschi, A. A. Katanin, A. E. Antipov, M. I. Katsnelson, A. I. Lichtenstein, A. N. Rubtsov,  and K. Held, “Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory,” Rev. Mod. Phys. 90, 025003 (2018).
  21. Ya. S. Lyakhova, G. V. Astretsov,  and A. N. Rubtsov, “The mean-field concept and post-DMFT methods in the contemporary theory of correlated systems,” PHYS-USP+  (2023), 10.3367/UFNe.2022.09.039231, [Phys. Usp. (2023)].
  22. S. Biermann, F. Aryasetiawan,  and A. Georges, “First-Principles Approach to the Electronic Structure of Strongly Correlated Systems: Combining the G⁢W𝐺𝑊GWitalic_G italic_W Approximation and Dynamical Mean-Field Theory,” Phys. Rev. Lett. 90, 086402 (2003).
  23. Ping Sun and Gabriel Kotliar, “Many-Body Approximation Scheme beyond GW,” Phys. Rev. Lett. 92, 196402 (2004).
  24. Thomas Ayral, Philipp Werner,  and Silke Biermann, “Spectral Properties of Correlated Materials: Local Vertex and Nonlocal Two-Particle Correlations from Combined G⁢W𝐺𝑊GWitalic_G italic_W and Dynamical Mean Field Theory,” Phys. Rev. Lett. 109, 226401 (2012).
  25. Thomas Ayral, Silke Biermann,  and Philipp Werner, “Screening and nonlocal correlations in the extended Hubbard model from self-consistent combined G⁢W𝐺𝑊GWitalic_G italic_W and dynamical mean field theory,” Phys. Rev. B 87, 125149 (2013).
  26. Li Huang, Thomas Ayral, Silke Biermann,  and Philipp Werner, “Extended dynamical mean-field study of the Hubbard model with long-range interactions,” Phys. Rev. B 90, 195114 (2014).
  27. L. Boehnke, F. Nilsson, F. Aryasetiawan,  and P. Werner, “When strong correlations become weak: Consistent merging of G⁢W𝐺𝑊GWitalic_G italic_W and DMFT,” Phys. Rev. B 94, 201106(R) (2016).
  28. Thomas Ayral, Silke Biermann, Philipp Werner,  and Lewin Boehnke, “Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory,” Phys. Rev. B 95, 245130 (2017a).
  29. A. N. Rubtsov, M. I. Katsnelson,  and A. I. Lichtenstein, “Dual fermion approach to nonlocal correlations in the Hubbard model,” Phys. Rev. B 77, 033101 (2008).
  30. A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein,  and A. Georges, “Dual fermion approach to the two-dimensional hubbard model: Antiferromagnetic fluctuations and fermi arcs,” Phys. Rev. B 79, 045133 (2009).
  31. H. Hafermann, G. Li, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein,  and H. Monien, “Efficient Perturbation Theory for Quantum Lattice Models,” Phys. Rev. Lett. 102, 206401 (2009).
  32. Sergei Iskakov, Andrey E. Antipov,  and Emanuel Gull, “Diagrammatic Monte Carlo for dual fermions,” Phys. Rev. B 94, 035102 (2016).
  33. Jan Gukelberger, Evgeny Kozik,  and Hartmut Hafermann, “Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory: Convergence analysis of the dual fermion technique,” Phys. Rev. B 96, 035152 (2017).
  34. Sergey Brener, Evgeny A. Stepanov, Alexey N. Rubtsov, Mikhail I. Katsnelson,  and Alexander I. Lichtenstein, “Dual fermion method as a prototype of generic reference-system approach for correlated fermions,” Ann. Phys. 422, 168310 (2020).
  35. A. N. Rubtsov, M. I. Katsnelson,  and A. I. Lichtenstein, “Dual boson approach to collective excitations in correlated fermionic systems,” Ann. Phys. 327, 1320 – 1335 (2012).
  36. Erik G. C. P. van Loon, Alexander I. Lichtenstein, Mikhail I. Katsnelson, Olivier Parcollet,  and Hartmut Hafermann, “Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model,” Phys. Rev. B 90, 235135 (2014).
  37. E. A. Stepanov, E. G. C. P. van Loon, A. A. Katanin, A. I. Lichtenstein, M. I. Katsnelson,  and A. N. Rubtsov, “Self-consistent dual boson approach to single-particle and collective excitations in correlated systems,” Phys. Rev. B 93, 045107 (2016a).
  38. E. A. Stepanov, A. Huber, E. G. C. P. van Loon, A. I. Lichtenstein,  and M. I. Katsnelson, “From local to nonlocal correlations: The Dual Boson perspective,” Phys. Rev. B 94, 205110 (2016b).
  39. Evgeny A. Stepanov, Lars Peters, Igor S. Krivenko, Alexander I. Lichtenstein, Mikhail I. Katsnelson,  and Alexey N. Rubtsov, “Quantum spin fluctuations and evolution of electronic structure in cuprates,” npj Quantum Mater. 3, 54 (2018).
  40. L. Peters, E. G. C. P. van Loon, A. N. Rubtsov, A. I. Lichtenstein, M. I. Katsnelson,  and E. A. Stepanov, “Dual boson approach with instantaneous interaction,” Phys. Rev. B 100, 165128 (2019).
  41. M. Vandelli, V. Harkov, E. A. Stepanov, J. Gukelberger, E. Kozik, A. Rubio,  and A. I. Lichtenstein, “Dual boson diagrammatic Monte Carlo approach applied to the extended Hubbard model,” Phys. Rev. B 102, 195109 (2020).
  42. A. Toschi, A. A. Katanin,  and K. Held, “Dynamical vertex approximation: A step beyond dynamical mean-field theory,” Phys. Rev. B 75, 045118 (2007).
  43. A. A. Katanin, A. Toschi,  and K. Held, “Comparing pertinent effects of antiferromagnetic fluctuations in the two- and three-dimensional Hubbard model,” Phys. Rev. B 80, 075104 (2009).
  44. Anna Galler, Patrik Thunström, Patrik Gunacker, Jan M. Tomczak,  and Karsten Held, “Ab initio dynamical vertex approximation,” Phys. Rev. B 95, 115107 (2017).
  45. Anna Galler, Josef Kaufmann, Patrik Gunacker, Matthias Pickem, Patrik Thunström, Jan M. Tomczak,  and Karsten Held, “Towards ab initio Calculations with the Dynamical Vertex Approximation,” J. Phys. Soc. Jpn. 87, 041004 (2018).
  46. Josef Kaufmann, Christian Eckhardt, Matthias Pickem, Motoharu Kitatani, Anna Kauch,  and Karsten Held, “Self-consistent ladder dynamical vertex approximation,” Phys. Rev. B 103, 035120 (2021).
  47. Thomas Ayral and Olivier Parcollet, “Mott physics and spin fluctuations: A unified framework,” Phys. Rev. B 92, 115109 (2015).
  48. Thomas Ayral and Olivier Parcollet, “Mott physics and spin fluctuations: A functional viewpoint,” Phys. Rev. B 93, 235124 (2016).
  49. J. Vučičević, T. Ayral,  and O. Parcollet, “TRILEX and G⁢W𝐺𝑊GWitalic_G italic_W+EDMFT approach to d𝑑ditalic_d-wave superconductivity in the Hubbard model,” Phys. Rev. B 96, 104504 (2017).
  50. Thomas Ayral, Jaksa Vučičević,  and Olivier Parcollet, “Fierz convergence criterion: A controlled approach to strongly interacting systems with small embedded clusters,” Phys. Rev. Lett. 119, 166401 (2017b).
  51. E. A. Stepanov, V. Harkov,  and A. I. Lichtenstein, “Consistent partial bosonization of the extended Hubbard model,” Phys. Rev. B 100, 205115 (2019).
  52. V. Harkov, M. Vandelli, S. Brener, A. I. Lichtenstein,  and E. A. Stepanov, “Impact of partially bosonized collective fluctuations on electronic degrees of freedom,” Phys. Rev. B 103, 245123 (2021).
  53. Matteo Vandelli, Josef Kaufmann, Mohammed El-Nabulsi, Viktor Harkov, Alexander I. Lichtenstein,  and Evgeny A. Stepanov, “Multi-band D-TRILEX approach to materials with strong electronic correlations,” SciPost Phys. 13, 036 (2022).
  54. Evgeny A. Stepanov, Yusuke Nomura, Alexander I. Lichtenstein,  and Silke Biermann, “Orbital Isotropy of Magnetic Fluctuations in Correlated Electron Materials Induced by Hund’s Exchange Coupling,” Phys. Rev. Lett. 127, 207205 (2021).
  55. E. A. Stepanov, V. Harkov, M. Rösner, A. I. Lichtenstein, M. I. Katsnelson,  and A. N. Rudenko, “Coexisting charge density wave and ferromagnetic instabilities in monolayer InSe,” npj Comput. Mater. 8, 118 (2022a).
  56. Evgeny A. Stepanov, “Eliminating Orbital Selectivity from the Metal-Insulator Transition by Strong Magnetic Fluctuations,” Phys. Rev. Lett. 129, 096404 (2022).
  57. M. Vandelli, A. Galler, A. Rubio, A. I. Lichtenstein, S. Biermann,  and E. A. Stepanov, “Doping-dependent charge- and spin-density wave orderings in a monolayer of Pb adatoms on Si(111),” Preprint arXiv:2301.07162 (2023b).
  58. Nikolai V. Prokof’ev and Boris V. Svistunov, “Polaron Problem by Diagrammatic Quantum Monte Carlo,” Phys. Rev. Lett. 81, 2514–2517 (1998).
  59. Riccardo Rossi, “Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit,” Phys. Rev. Lett. 119, 045701 (2017).
  60. Fedor Šimkovic and Evgeny Kozik, “Determinant Monte Carlo for irreducible Feynman diagrams in the strongly correlated regime,” Phys. Rev. B 100, 121102(R) (2019).
  61. Aaram J. Kim, Fedor Simkovic,  and Evgeny Kozik, “Spin and Charge Correlations across the Metal-to-Insulator Crossover in the Half-Filled 2D Hubbard Model,” Phys. Rev. Lett. 124, 117602 (2020).
  62. Thomas Schäfer, Nils Wentzell, Fedor Šimkovic, Yuan-Yao He, Cornelia Hille, Marcel Klett, Christian J. Eckhardt, Behnam Arzhang, Viktor Harkov, François-Marie Le Régent, Alfred Kirsch, Yan Wang, Aaram J. Kim, Evgeny Kozik, Evgeny A. Stepanov, Anna Kauch, Sabine Andergassen, Philipp Hansmann, Daniel Rohe, Yuri M. Vilk, James P. F. LeBlanc, Shiwei Zhang, A.-M. S. Tremblay, Michel Ferrero, Olivier Parcollet,  and Antoine Georges, “Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model,” Phys. Rev. X 11, 011058 (2021).
  63. J. P. F. LeBlanc, Andrey E. Antipov, Federico Becca, Ireneusz W. Bulik, Garnet Kin-Lic Chan, Chia-Min Chung, Youjin Deng, Michel Ferrero, Thomas M. Henderson, Carlos A. Jiménez-Hoyos, E. Kozik, Xuan-Wen Liu, Andrew J. Millis, N. V. Prokof’ev, Mingpu Qin, Gustavo E. Scuseria, Hao Shi, B. V. Svistunov, Luca F. Tocchio, I. S. Tupitsyn, Steven R. White, Shiwei Zhang, Bo-Xiao Zheng, Zhenyue Zhu,  and Emanuel Gull (Simons Collaboration on the Many-Electron Problem), “Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms,” Phys. Rev. X 5, 041041 (2015).
  64. Jan Gukelberger, Li Huang,  and Philipp Werner, “On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime,” Phys. Rev. B 91, 235114 (2015).
  65. John Hubbard, “Electron correlations in narrow energy bands,” Proc. R. Soc. A: Math. Phys. Eng. Sci. 276, 238–257 (1963).
  66. Josef Kaufmann and Karsten Held, “ana_cont: Python package for analytic continuation,” Preprint arXiv:2105.11211 (2021).
  67. E. A. Stepanov, S. Brener, V. Harkov, M. I. Katsnelson,  and A. I. Lichtenstein, “Spin dynamics of itinerant electrons: Local magnetic moment formation and Berry phase,” Phys. Rev. B 105, 155151 (2022b).
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