- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Determinantal quantum Monte Carlo solver for cluster perturbation theory

Edwin W. Huang1,*, Shuhan Ding2, Jiarui Liu2, and Yao Wang2,†

  • 1Department of Physics and Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 2Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29631, USA

  • *edwinwhuang@gmail.com
  • †yaowang@g.clemson.edu
PDF

Phys. Rev. Research 4, L042015 – Published 26 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042015

Abstract

Cluster perturbation theory (CPT) is a technique for computing the spectral function of fermionic models with local interactions. By combining the solution of the model on a finite cluster with perturbation theory on intracluster hoppings, CPT provides access to single-particle properties with arbitrary momentum resolution while incurring low computational cost. Here, we introduce determinantal quantum Monte Carlo (DQMC) as a solver for CPT. Compared to the standard solver, exact diagonalization (ED), the DQMC solver reduces finite size effects through utilizing larger clusters, allows study of temperature dependence, and enables large-scale simulations of a greater set of models. We discuss the implementation of the DQMC solver for CPT and benchmark the CPT + DQMC method for the attractive and repulsive Hubbard models, showcasing its advantages over standard DQMC and CPT + ED simulations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

  1. A. Damascelli, Z. Hussain, and Z.-X. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Rev. Mod. Phys. 75, 473 (2003).
  2. J. A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).
  3. N. E. Bickers, D. J. Scalapino, and S. R. White, Conserving Approximations for Strongly Correlated Electron Systems: Bethe-Salpeter Equation and Dynamics for the Two-Dimensional Hubbard Model, Phys. Rev. Lett. 62, 961 (1989).
  4. 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 (2006).
  5. Q. Li, J. Callaway, and L. Tan, Spectral function in the two-dimensional Hubbard model, Phys. Rev. B 44, 10256 (1991).
  6. E. Dagotto, F. Ortolani, and D. Scalapino, Single-particle spectral weight of a two-dimensional Hubbard model, Phys. Rev. B 46, 3183 (1992).
  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. S. R. White, D. J. Scalapino, R. L. Sugar, E. Y. Loh, J. E. Gubernatis, and R. T. Scalettar, Numerical Study of the Two-Dimensional Hubbard Model, Phys. Rev. B 40, 506 (1989).
  9. S. R. White, Density Matrix Formulation for Quantum Renormalization Groups, Phys. Rev. Lett. 69, 2863 (1992).
  10. S. R. White and A. E. Feiguin, Real-Time Evolution Using the Density Matrix Renormalization Group, Phys. Rev. Lett. 93, 076401 (2004).
  11. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
  12. T. Maier, M. Jarrell, T. Pruschke, and M. H. Hettler, Quantum cluster theories, Rev. Mod. Phys. 77, 1027 (2005).
  13. S. Pairault, D. Sénéchal, and A.-M. S. Tremblay, Strong-Coupling Expansion for the Hubbard Model, Phys. Rev. Lett. 80, 5389 (1998).
  14. D. Sénéchal, D. Perez, and M. Pioro-Ladrière, Spectral Weight of the Hubbard Model through Cluster Perturbation Theory, Phys. Rev. Lett. 84, 522 (2000).
  15. D. Sénéchal, D. Perez, and D. Plouffe, Cluster perturbation theory for Hubbard models, Phys. Rev. B 66, 075129 (2002).
  16. D. Sénéchal, Cluster perturbation theory, in Strongly Correlated Systems (Springer, Berlin - Heidelberg, 2012), pp. 237–270.
  17. C. Gros and R. Valenti, Cluster expansion for the self-energy: A simple many-body method for interpreting the photoemission spectra of correlated fermi systems, Phys. Rev. B 48, 418 (1993).
  18. D. Sénéchal and A.-M. S. Tremblay, Hot Spots and Pseudogaps for Hole- and Electron-Doped High-Temperature Superconductors, Phys. Rev. Lett. 92, 126401 (2004).
  19. W.-Q. Ning, H. Zhao, C.-Q. Wu, and H.-Q. Lin, Phonon Effects on Spin-Charge Separation in One Dimension, Phys. Rev. Lett. 96, 156402 (2006).
  20. M. Kohno, Mott Transition in the Two-Dimensional Hubbard Model, Phys. Rev. Lett. 108, 076401 (2012).
  21. V. I. Kuz'min, S. V. Nikolaev, and S. G. Ovchinnikov, Comparison of the electronic structure of the Hubbard and t−J models within the cluster perturbation theory, Phys. Rev. B 90, 245104 (2014).
  22. M. Kohno, Spectral properties near the Mott transition in the two-dimensional Hubbard model with next-nearest-neighbor hopping, Phys. Rev. B 90, 035111 (2014).
  23. Y. Wang, K. Wohlfeld, B. Moritz, C. J. Jia, M. van Veenendaal, K. Wu, C.-C. Chen, and T. P. Devereaux, Origin of strong dispersion in Hubbard insulators, Phys. Rev. B 92, 075119 (2015).
  24. M. Kohno, Spectral properties near the mott transition in the two-dimensional t−J model, Phys. Rev. B 92, 085128 (2015).
  25. Y. Wang, B. Moritz, C.-C. Chen, T. P. Devereaux, and K. Wohlfeld, Influence of magnetism and correlation on the spectral properties of doped Mott insulators, Phys. Rev. B 97, 115120 (2018).
  26. V. Kuz'min, S. Nikolaev, and S. Ovchinnikov, Effect of short-range correlations on spectral properties of doped Mott insulators, J. Supercond. Novel Magn. 32, 1909 (2019).
  27. V. I. Kuz'min, M. A. Visotin, S. V. Nikolaev, and S. G. Ovchinnikov, Doping and temperature evolution of pseudogap and spin-spin correlations in the two-dimensional Hubbard model, Phys. Rev. B 101, 115141 (2020).
  28. Y. Wang, Y. He, K. Wohlfeld, M. Hashimoto, E. W. Huang, D. Lu, S.-K. Mo, S. Komiya, C. Jia, B. Moritz et al., Emergence of quasiparticles in a doped Mott insulator, Commun. Phys. 3, 1 (2020).
  29. C. Yang and A. E. Feiguin, Spectral function of the two-dimensional Hubbard model: A density matrix renormalization group plus cluster perturbation theory study, Phys. Rev. B 93, 081107(R) (2016).
  30. M. Jarrell and J. E. Gubernatis, Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data, Phys. Rep. 269, 133 (1996).
  31. D. Bergeron and A.-M. S. Tremblay, Algorithms for optimized maximum entropy and diagnostic tools for analytic continuation, Phys. Rev. E 94, 023303 (2016).
  32. T. Paiva, R. R. dos Santos, R. T. Scalettar, and P. J. H. Denteneer, Critical temperature for the two-dimensional attractive Hubbard model, Phys. Rev. B 69, 184501 (2004).
  33. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.4.L042015 for a detailed discussion about the reduction of finite-size effects, benchmarks for a 1D system, extensions to complicated systems, and spectral quantities besides A(k,ω).
  34. Only the removal spectra is plotted because particle-hole symmetry guarantees A(k,ω)=A(k+Q,−ω) where Q=(π,π).
  35. M. Kohno, Spectral Properties near the Mott Transition in the One-Dimensional Hubbard Model, Phys. Rev. Lett. 105, 106402 (2010).
  36. A. Nocera, F. H. L. Essler, and A. E. Feiguin, Finite-temperature dynamics of the Mott insulating Hubbard chain, Phys. Rev. B 97, 045146 (2018).
  37. J. P. F. LeBlanc, A. E. Antipov, F. Becca, I. W. Bulik, G. K.-L. Chan, C.-M. Chung, Y. Deng, M. Ferrero, T. M. Henderson, C. A. Jiménez-Hoyos, E. Kozik, X.-W. Liu, A. J. Millis, N. V. Prokof'ev, M. Qin, G. E. Scuseria, H. Shi, B. V. Svistunov, L. F. Tocchio, I. S. Tupitsyn et al., Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms, Phys. Rev. X 5, 041041 (2015).
  38. E. Y. Loh, J. E. Gubernatis, R. T. Scalettar, S. R. White, D. J. Scalapino, and R. L. Sugar, Sign problem in the numerical simulation of many-electron systems, Phys. Rev. B 41, 9301 (1990).
  39. V. I. Iglovikov, E. Khatami, and R. T. Scalettar, Geometry dependence of the sign problem in quantum Monte Carlo simulations, Phys. Rev. B 92, 045110 (2015).
  40. W. E. Ormand, D. J. Dean, C. W. Johnson, G. H. Lang, and S. E. Koonin, Demonstration of the auxiliary-field Monte Carlo approach for sd-shell nuclei, Phys. Rev. C 49, 1422 (1994).
  41. S. Nath and N. Ghosh, Phonon-mediated electron–phonon interaction in Hubbard–Holstein model, J. Low Temp. Phys. 182, 1 (2016).
  42. S. Nath, N. Mondal, and N. Ghosh, Interplay between electron-phonon interaction and Hubbard repulsion: An exact approach, J. Supercond. Novel Magn. 28, 1687 (2015).
  43. A. Payeur and D. Sénéchal, Variational cluster approximation study of the one-dimensional Holstein-Hubbard model at half filling, Phys. Rev. B 83, 033104 (2011).
  44. Y. Wang, B. Moritz, C.-C. Chen, C. J. Jia, M. van Veenendaal, and T. P. Devereaux, Using Nonequilibrium Dynamics to Probe Competing Orders in a Mott-Peierls System, Phys. Rev. Lett. 116, 086401 (2016).
  45. Y. Wang, C.-C. Chen, B. Moritz, and T. P. Devereaux, Light-Enhanced Spin Fluctuations and d-Wave Superconductivity at a Phase Boundary, Phys. Rev. Lett. 120, 246402 (2018).
  46. C. Wu and S.-C. Zhang, Sufficient condition for absence of the sign problem in the fermionic quantum Monte Carlo algorithm, Phys. Rev. B 71, 155115 (2005).
  47. X.-X. Huang, M. Claassen, E. W. Huang, B. Moritz, and T. P. Devereaux, Biexciton Condensation in Electron-Hole-Doped Hubbard Bilayers: A Sign-Problem-Free Quantum Monte Carlo Study, Phys. Rev. Lett. 124, 077601 (2020).

Outline

Information

Phys. Rev. Research 4, L042015– Published 26 October, 2022
  • Received 14 October 2021
  • Accepted 14 September 2022
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation