Papers
Topics
Authors
Recent
Search
2000 character limit reached

Worldline Monte Carlo method for few body nuclear physics

Published 23 Feb 2024 in nucl-th and hep-lat | (2402.15377v1)

Abstract: In this work we introduce a worldline based fermion Monte Carlo algorithm for studying few body quantum mechanics of self-interacting fermions in the Hamiltonian lattice formulation. Our motivation to construct the method comes from our interest in studying renormalization of chiral nuclear effective field theory with lattice regularization. In particular we wish to apply our method to compute the lattice spacing dependence of local lattice interactions as we take the continuum limit of the lattice theory. Our algorithm can compute matrix elements of the operator $\exp(-\beta H)$ where $H$ is the lattice Hamiltonian and $\beta$ is a free real parameter. These elements help us compute deep bound states that are well separated from scattering states even at values of $\beta$ which are not very large. Computing these bound state energies accurately can help us study renormalization of the lattice theory. In addition to developing the algorithm, in this work we also introduce a finite volume renormalization scheme for the lattice Hamiltonian of the leading pionless effective field theory and show how it would work in the one and two body sectors.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (54)
  1. D. Ceperley, G. V. Chester, and M. H. Kalos, Monte carlo simulation of a many-fermion study, Phys. Rev. B 16, 3081 (1977).
  2. M. Troyer and U.-J. Wiese, Computational complexity and fundamental limitations to fermionic quantum monte carlo simulations, Phys. Rev. Lett. 94, 170201 (2005).
  3. U. J. Wiese, Bosonization and cluster updating of lattice fermions, Phys. Lett. B 311, 235 (1993), arXiv:hep-lat/9210019 .
  4. H. Singh and S. Chandrasekharan, Few-body physics on a spacetime lattice in the worldline approach, Phys. Rev. D 99, 074511 (2019).
  5. S. Zhang, J. Carlson, and J. E. Gubernatis, A Constrained path Monte Carlo method for fermion ground states, Phys. Rev. B 55, 7464 (1997), arXiv:cond-mat/9607062 .
  6. S. Zhang, Auxiliary-field quantum monte carlo for correlated electron systems, in Emergent Phenomena in Correlated Matter, edited by E. Pavarini, E. Koch, and U. Schollwöck (Verlag des Forschungszentrum Jülich, 2013).
  7. R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Monte carlo calculations of coupled boson-fermion systems. i, Phys. Rev. D 24, 2278 (1981).
  8. R. T. Scalettar, D. J. Scalapino, and R. L. Sugar, New algorithm for the numerical simulation of fermions, Phys. Rev. B 34, 7911 (1986).
  9. A. D. Kennedy, Algorithms for lattice QCD with dynamical fermions, Nucl. Phys. B Proc. Suppl. 140, 190 (2005), arXiv:hep-lat/0409167 .
  10. D. Lee, Lattice simulations for few- and many-body systems, Prog. Part. Nucl. Phys. 63, 117 (2009), arXiv:0804.3501 [nucl-th] .
  11. J. E. Drut and A. N. Nicholson, Lattice methods for strongly interacting many-body systems, Journal of Physics G: Nuclear and Particle Physics 40, 043101 (2013).
  12. E. F. Huffman and S. Chandrasekharan, Solution to sign problems in half-filled spin-polarized electronic systems, Phys. Rev. B 89, 111101 (2014).
  13. Z.-X. Li, Y.-F. Jiang, and H. Yao, Solving the fermion sign problem in quantum monte carlo simulations by majorana representation, Phys. Rev. B 91, 241117 (2015).
  14. Z.-X. Li, Y.-F. Jiang, and H. Yao, Majorana-time-reversal symmetries: A fundamental principle for sign-problem-free quantum monte carlo simulations, Phys. Rev. Lett. 117, 267002 (2016).
  15. D. M. Ceperley, Path integrals in the theory of condensed helium, Rev. Mod. Phys. 67, 279 (1995).
  16. N. Prokof’ev and B. Svistunov, Worm algorithms for classical statistical models, Phys. Rev. Lett. 87, 160601 (2001).
  17. O. F. Syljuåsen and A. W. Sandvik, Quantum monte carlo with directed loops, Phys. Rev. E 66, 046701 (2002).
  18. D. H. Adams and S. Chandrasekharan, Chiral limit of strongly coupled lattice gauge theories, Nucl. Phys. B662, 220 (2003).
  19. J. Frank, E. Huffman, and S. Chandrasekharan, Emergence of Gauss’ law in a Z2subscript𝑍2Z_{2}italic_Z start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT lattice gauge theory in 1 + 1 dimensions, Phys. Lett. B 806, 135484 (2020), arXiv:1904.05414 [cond-mat.str-el] .
  20. S. Chandrasekharan and U.-J. Wiese, Meron-cluster solution of fermion sign problems, Phys. Rev. Lett. 83, 3116 (1999).
  21. S. Chandrasekharan, Fermion bag approach to lattice field theories, Phys. Rev. D 82, 025007 (2010).
  22. E. Huffman and S. Chandrasekharan, Fermion-bag inspired hamiltonian lattice field theory for fermionic quantum criticality, Phys. Rev. D 101, 074501 (2020).
  23. D. Lee, Permutation zones and the fermion sign problem, arXiv:cond-mat/0202283  (2002).
  24. D. B. Kaplan, M. J. Savage, and M. B. Wise, A New expansion for nucleon-nucleon interactions, Phys. Lett. B 424, 390 (1998), arXiv:nucl-th/9801034 .
  25. D. B. Kaplan, M. J. Savage, and M. B. Wise, Nucleon - nucleon scattering from effective field theory, Nucl. Phys. B 478, 629 (1996), arXiv:nucl-th/9605002 .
  26. P. F. Bedaque, H. W. Hammer, and U. van Kolck, Renormalization of the three-body system with short range interactions, Phys. Rev. Lett. 82, 463 (1999a), arXiv:nucl-th/9809025 .
  27. P. F. Bedaque, H. W. Hammer, and U. van Kolck, The Three boson system with short range interactions, Nucl. Phys. A 646, 444 (1999b), arXiv:nucl-th/9811046 .
  28. P. F. Bedaque, H. W. Hammer, and U. van Kolck, Effective theory of the triton, Nucl. Phys. A 676, 357 (2000), arXiv:nucl-th/9906032 .
  29. E. Epelbaum, H.-W. Hammer, and U.-G. Meissner, Modern Theory of Nuclear Forces, Rev. Mod. Phys. 81, 1773 (2009a), arXiv:0811.1338 [nucl-th] .
  30. H. W. Hammer, S. König, and U. van Kolck, Nuclear effective field theory: status and perspectives, Rev. Mod. Phys. 92, 025004 (2020), arXiv:1906.12122 [nucl-th] .
  31. A. M. Gasparyan and E. Epelbaum, “Renormalization-group-invariant effective field theory” for few-nucleon systems is cutoff dependent, Phys. Rev. C 107, 034001 (2023), arXiv:2210.16225 [nucl-th] .
  32. C. Körber, E. Berkowitz, and T. Luu, Renormalization of a Contact Interaction on a Lattice, arXiv:1912.04425  (2019).
  33. D. Lee and T. Schäfer, Neutron matter on the lattice with pionless effective field theory, Phys. Rev. C 72, 024006 (2005), arXiv:nucl-th/0412002 .
  34. D. Lee, B. Borasoy, and T. Schäfer, Nuclear lattice simulations with chiral effective field theory, Phys. Rev. C 70, 014007 (2004), arXiv:nucl-th/0402072 .
  35. D. Lee and T. Schäfer, Cold dilute neutron matter on the lattice. I. Lattice virial coefficients and large scattering lengths, Phys. Rev. C 73, 015201 (2006a), arXiv:nucl-th/0509017 .
  36. D. Lee and T. Schäfer, Cold dilute neutron matter on the lattice. II. Results in the unitary limit, Phys. Rev. C 73, 015202 (2006b), arXiv:nucl-th/0509018 .
  37. D. Lee, The Ground state energy at unitarity, Phys.Rev. C78, 024001 (2008), arXiv:0803.1280 [nucl-th] .
  38. D. Lee, Recent Progress in Nuclear Lattice Simulations, Front. in Phys. 8, 174 (2020).
  39. D. Lee, Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations, Few Body Syst. 62, 115 (2021), arXiv:2109.09582 [nucl-th] .
  40. N. Klein, D. Lee, and U.-G. Meißner, Lattice Improvement in Lattice Effective Field Theory, Eur. Phys. J. A 54, 233 (2018a), arXiv:1807.04234 [hep-lat] .
  41. S. Elhatisari et al., Wave function matching for the quantum many-body problem, arXiv:2210.17488  (2022).
  42. M. Eliyahu, B. Bazak, and N. Barnea, Extrapolating Lattice QCD Results using Effective Field Theory, Phys. Rev. C 102, 044003 (2020), arXiv:1912.07017 [nucl-th] .
  43. W. Detmold and P. E. Shanahan, Few-nucleon matrix elements in pionless effective field theory in a finite volume, Phys. Rev. D 103, 074503 (2021), arXiv:2102.04329 [nucl-th] .
  44. W. Detmold, F. Romero-López, and P. E. Shanahan, Constraint of pionless EFT using two-nucleon spectra from lattice QCD, Phys. Rev. D 108, 034509 (2023), arXiv:2305.06313 [nucl-th] .
  45. G. P. Lepage, How to renormalize the Schrodinger equation, in 8th Jorge Andre Swieca Summer School on Nuclear Physics (1997) pp. 135–180, arXiv:nucl-th/9706029 .
  46. G. Joyce and I. Zucker, On the evaluation of generalized watson integrals, Proceedings of the American Mathematical Society 133, 71 (2005).
  47. E. Braaten and H. W. Hammer, Universality in few-body systems with large scattering length, Phys. Rept. 428, 259 (2006), arXiv:cond-mat/0410417 .
  48. B. Blankleider and J. Gegelia, Three body system in leading order effective field theory without three body forces, arXiv:nucl-th/0009007  (2000), arXiv:nucl-th/0009007 .
  49. L. Platter, H. W. Hammer, and U.-G. Meissner, The Four boson system with short range interactions, Phys. Rev. A 70, 052101 (2004), arXiv:cond-mat/0404313 .
  50. X. Lin, Four-Body Systems at Large Cutoffs in Effective Field Theory, arXiv:2304.06172  (2023).
  51. C. Michael, Adjoint Sources in Lattice Gauge Theory, Nucl. Phys. B 259, 58 (1985).
  52. M. Luscher and U. Wolff, How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation, Nucl. Phys. B 339, 222 (1990).
  53. P. Naidon and S. Endo, Efimov Physics: a review, Rept. Prog. Phys. 80, 056001 (2017), arXiv:1610.09805 [quant-ph] .
  54. P. de Forcrand, B. Lucini, and M. Vettorazzo, Measuring interface tensions in 4d SU(N) lattice gauge theories, Nucl. Phys. B Proc. Suppl. 140, 647 (2005), arXiv:hep-lat/0409148 .

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 1 like about this paper.

Sign Up for Free