Perturbative solution of fermionic sign problem in quantum Monte Carlo computations
Source abstract
Abstract
Abstract We have developed a strong-coupling perturbation scheme for a general doped Hubbard model around a particle-hole-symmetric reference system, which is free from the fermionic sign problem. Our approach is based on the lattice determinantal Quantum Monte Carlo (QMC) method in both continuous and discrete time versions for large periodic clusters in a fermionic bath. By considering the first-order perturbation in the shift of the chemical potential and the second-neighbor hopping, we are able to obtain an accurate electronic spectral function for a range of parameters that correspond to optimally doped cuprate systems at temperatures of up to T = 0.1 t , which are challenging to access using straightforward lattice QMC calculations. We also discuss the formation of the pseudogap and the nodal-antinodal dichotomy for a doped Hubbard system with the interaction parameter U equal to the bandwidth and the optimal value of the next-nearest-neighbor hopping parameter $${t}^{{\prime} }$$ for high-temperature superconducting cuprates.
Source: crossref · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Physics of Superconductivity and Magnetism · Quantum and electron transport phenomena · Magnetic and transport properties of perovskites and related materials
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (52)
Show source-provided references
1. Schäfer, T. et al. Tracking the footprints of spin fluctuations: a multimethod, multimessenger study of the two-dimensional Hubbard model. Phys. Rev. X 11, 011058 (2021).
2. De Raedt, H. & Lagendijk, A. Monte Carlo simulation of quantum statistical lattice models. Phys. Rep. 127, 233–307 (1985).10.1016/0370-1573(85)90044-4 ↗
3. Loh, E. Y. et al. Sign problem in the numerical simulation of many-electron systems. Phys. Rev. B 41, 9301–9307 (1990).10.1103/PhysRevB.41.9301 ↗
4. Troyer, M. & Wiese, U.-J. Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94, 170201 (2005).10.1103/PhysRevLett.94.170201 ↗
5. Mondaini, R., Tarat, S. & Scalettar, R. T. Quantum critical points and the sign problem. Science 375, 418–424 (2022).10.1126/science.abg9299 ↗
6. Jiang, H.-C. & Devereaux, T. P. Superconductivity in the doped Hubbard model and its interplay with next-nearest hopping t’. Science 365, 1424–1428 (2019).10.1126/science.aal5304 ↗
7. Jiang, Y.-F., Zaanen, J., Devereaux, T. P. & Jiang, H.-C. Ground state phase diagram of the doped Hubbard model on the four-leg cylinder. Phys. Rev. Res. 2, 033073 (2020).10.1103/PhysRevResearch.2.033073 ↗
8. Chung, C.-M., Qin, M., Zhang, S., Schollwöck, U. & White, S. R. Plaquette versus ordinary d-wave pairing in the $${t}^{{\prime} }$$-Hubbard model on a width-4 cylinder. Phys. Rev. B 102, 041106 (2020).10.1103/PhysRevB.102.041106 ↗
9. Qin, M. et al. Absence of superconductivity in the pure two-dimensional Hubbard model. Phys. Rev. X 10, 031016 (2020).
10. Harland, M., Katsnelson, M. I. & Lichtenstein, A. I. Plaquette valence bond theory of high-temperature superconductivity. Phys. Rev. B 94, 125133 (2016).10.1103/PhysRevB.94.125133 ↗
11. Harland, M., Brener, S., Katsnelson, M. I. & Lichtenstein, A. I. Exactly solvable model of strongly correlated d-wave superconductivity. Phys. Rev. B 101, 045119 (2020).10.1103/PhysRevB.101.045119 ↗
12. Danilov, M. et al. Degenerate plaquette physics as key ingredient of high-temperature superconductivity in cuprates. npj Quant. Mater. 7, 50 (2022).10.1038/s41535-022-00454-6 ↗
13. Schmid, M. T., Morée, J.-B., Kaneko, R., Yamaji, Y. & Imada, M. Superconductivity studied by solving ab initio low-energy effective Hamiltonians for carrier doped cacuo2, bi2sr2cuo6, bi2sr2cacu2o8, and hgba2cuo4. Phys. Rev. X 13, 041036 (2023).
14. Xu, H. et al. Coexistence of superconductivity with partially filled stripes in the Hubbard model. Preprint at https://arxiv.org/abs/2303.08376 (2023).
15. Prokof’ev, N. & Svistunov, B. Bold diagrammatic Monte Carlo technique: When the sign problem is welcome. Phys. Rev. Lett. 99, 250201 (2007).10.1103/PhysRevLett.99.250201 ↗
16. Rossi, R. Determinant diagrammatic Monte Carlo algorithm in the thermodynamic limit. Phys. Rev. Lett. 119, 045701 (2017).10.1103/PhysRevLett.119.045701 ↗
17. Rubtsov, A. N., Savkin, V. V. & Lichtenstein, A. I. Continuous-time quantum Monte Carlo method for fermions. Phys. Rev. B 72, 035122 (2005).10.1103/PhysRevB.72.035122 ↗
18. Šimkovic, F., Rossi, R., Georges, A. & Ferrero, M. Origin and fate of the pseudogap in the doped Hubbard model. Preprint at http://arxiv.org/abs/2209.09237 (2022).
19. Šimkovic, F., Rossi, R. & Ferrero, M. Two-dimensional Hubbard model at finite temperature: weak, strong, and long correlation regimes. Phys. Rev. Res. 4, 043201 (2022).10.1103/PhysRevResearch.4.043201 ↗
20. Rossi, R., Prokof’ev, N., Svistunov, B., Houcke, K. V. & Werner, F. Polynomial complexity despite the fermionic sign. Europhys. Lett. 118, 10004 (2017).10.1209/0295-5075/118/10004 ↗
21. Kim, A. J., Prokof’ev, N. V., Svistunov, B. V. & Kozik, E. Homotopic action: a pathway to convergent diagrammatic theories. Phys. Rev. Lett. 126, 257001 (2021).10.1103/PhysRevLett.126.257001 ↗
22. Charlebois, M. & Imada, M. Single-particle spectral function formulated and calculated by variational Monte Carlo method with application to d-wave superconducting state. Phys. Rev. X 10, 041023 (2020).
23. Rosenberg, P., Sénéchal, D., Tremblay, A.-M. S. & Charlebois, M. Fermi arcs from dynamical variational Monte Carlo. Phys. Rev. B 106, 245132 (2022).10.1103/PhysRevB.106.245132 ↗
24. Sakai, S., Civelli, M. & Imada, M. Hidden fermionic excitation boosting high-temperature superconductivity in cuprates. Phys. Rev. Lett. 116, 057003 (2016).10.1103/PhysRevLett.116.057003 ↗
25. Singh, A. et al. Unconventional exciton evolution from the pseudogap to superconducting phases in cuprates. Nat. Commun. 13, 7906 (2022).10.1038/s41467-022-35210-8 ↗
26. Vidhyadhiraja, N. S., Macridin, A., Şen, C., Jarrell, M. & Ma, M. Quantum critical point at finite doping in the 2d Hubbard model: A dynamical cluster quantum Monte Carlo study. Phys. Rev. Lett. 102, 206407 (2009).10.1103/PhysRevLett.102.206407 ↗
27. Chen, K.-S., Meng, Z. Y., Pruschke, T., Moreno, J. & Jarrell, M. Lifshitz transition in the two-dimensional Hubbard model. Phys. Rev. B 86, 165136 (2012).10.1103/PhysRevB.86.165136 ↗
28. Krien, F., Worm, P., Chalupa-Gantner, P., Toschi, A. & Held, K. Explaining the pseudogap through damping and antidamping on the fermi surface by imaginary spin scattering. Commun. Phys. 5, 336 (2022).10.1038/s42005-022-01117-5 ↗
29. Brener, S., Stepanov, E. A., Rubtsov, A. N., Katsnelson, M. I. & Lichtenstein, A. I. Dual fermion method as a prototype of generic reference-system approach for correlated fermions. Annal. Phys. 422, 168310 (2020).10.1016/j.aop.2020.168310 ↗
30. Abrikosov, A. A., Gorkov, L. P. & Dzyaloshinski, I. E. Methods of Quantum Field Theory in Statistical Physics. (Dover, New York, NY, 1975).
31. Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996).10.1103/RevModPhys.68.13 ↗
32. Rubtsov, A. N., Katsnelson, M. I. & Lichtenstein, A. I. Dual fermion approach to nonlocal correlations in the Hubbard model. Phys. Rev. B 77, 033101 (2008).10.1103/PhysRevB.77.033101 ↗
33. Bethe, H. A & Jackiw, R. W. Intermediate Quantum Mechanics 3rd edn. (Taylor and Francis, 1986).
34. Katsnelson, M. I. & Irkhin, V. Y. Metal-insulator transition and antiferromagnetism in the ground state of the Hubbard model. J. Phys. C 17, 4291–4308 (1984).10.1088/0022-3719/17/24/011 ↗
35. Irkhin, V. Y. & Katsnelson, M. I. On the ground state wave function of a superconductor in the BCS model. Phys. Lett. A 104, 163–165 (1984).10.1016/0375-9601(84)90368-2 ↗
36. Irkhin, V. Y. & Katsnelson, M. I. Theory of intermediate-valence semiconductors. Sov. Phys. JETP 63, 631–636 (1986).
37. Peierls, R. On a minimum property of the free energy. Phys. Rev. 54, 918–919 (1938).10.1103/PhysRev.54.918 ↗
38. Feynman, R. P. Statistical Mechanics: A Set of Lectures (Benjamin/Cummings, 1972).
39. Bogolyubov, N. N. On a variational principle in the many-body problem. Sov. Phys. Dokl. 3, 292–294 (1958).
40. Scalettar, R. T., Noack, R. M. & Singh, R. R. P. Ergodicity at large couplings with the determinant Monte Carlo algorithm. Phys. Rev. B 44, 10502–10507 (1991).10.1103/PhysRevB.44.10502 ↗
41. Rohringer, G. et al. Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory. Rev. Mod. Phys. 90, 025003 (2018).10.1103/RevModPhys.90.025003 ↗
42. Rost, D., Gorelik, E. V., Assaad, F. & Blümer, N. Momentum-dependent pseudogaps in the half-filled two-dimensional Hubbard model. Phys. Rev. B 86, 155109 (2012).10.1103/PhysRevB.86.155109 ↗
43. Fei, J., Yeh, C.-N., Zgid, D. & Gull, E. Analytical continuation of matrix-valued functions: Carathéodory formalism. Phys. Rev. B 104, 165111 (2021).10.1103/PhysRevB.104.165111 ↗
44. Hirsch, J. E. & Fye, R. M. Monte Carlo method for magnetic impurities in metals. Phys. Rev. Lett. 56, 2521–2524 (1986).10.1103/PhysRevLett.56.2521 ↗
45. Wu, W., Ferrero, M., Georges, A. & Kozik, E. Controlling Feynman diagrammatic expansions: physical nature of the pseudogap in the two-dimensional Hubbard model. Phys. Rev. B 96, 041105 (2017).10.1103/PhysRevB.96.041105 ↗
46. Rossi, R., Šimkovic, F. & Ferrero, M. Renormalized perturbation theory at large expansion orders. Europhys. Lett. 132, 11001 (2020).10.1209/0295-5075/132/11001 ↗
47. Grossman, O. & Berg, E. Robust fermi-liquid instabilities in sign problem-free models. Phys. Rev. Lett. 131, 056501 (2023).10.1103/PhysRevLett.131.056501 ↗
48. Zhang, X., Pan, G., Xu, X. Y. & Meng, Z. Y. Fermion sign bounds theory in quantum Monte Carlo simulation. Phys. Rev. B 106, 035121 (2022).10.1103/PhysRevB.106.035121 ↗
49. Zhang, X. et al. Polynomial sign problem and topological mott insulator in twisted bilayer graphene. Phys. Rev. B 107, L241105 (2023).10.1103/PhysRevB.107.L241105 ↗
50. Hafermann, H., Brener, S., Rubtsov, A. N., Katsnelson, M. I. & Lichtenstein, A. I. Cluster dual fermion approach to nonlocal correlations. JETP Lett. 86, 677–682 (2008).10.1134/S0021364007220134 ↗
51. Pairault, S., Sénéchal, D. & Tremblay, A.-M. S. Strong-coupling expansion for the Hubbard model. Phys. Rev. Lett. 80, 5389–5392 (1998).10.1103/PhysRevLett.80.5389 ↗
52. Gros, C. & Valentí, R. Cluster expansion for the self-energy: a simple many-body method for interpreting the photoemission spectra of correlated fermi systems. Phys. Rev. B 48, 418–425 (1993).10.1103/PhysRevB.48.418 ↗