Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models (2405.06440v3)
Abstract: Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo (QMC) sampling suffers from the sign problem, e.g., when solving a multiorbital quantum impurity model. Recently, two approaches have been proposed for efficient numerical treatment of Feynman diagrams: Tensor Cross Interpolation (TCI) for replacing the stochastic sampling and the Quantics Tensor Train (QTT) representation for compressing space-time dependence. Combining these approaches, we find low-rank structures in weak-coupling Feynman diagrams for a multiorbital electron-phonon model and demonstrate their efficient numerical integrations with exponential resolution in time and exponential convergence of error with respect to computational cost.
- G. D. Mahan, Many-Particle Physics (Kluwer Academic/Plenum Publishers, New York, 2000).
- J. E. Hirsch and R. M. Fye, Monte carlo method for magnetic impurities in metals, Physical review letters 56, 2521 (1986).
- N. Prokof’ev and B. Svistunov, Bold diagrammatic monte carlo technique: When the sign problem is welcome, Physical review letters 99, 250201 (2007).
- G. Pan and Z. Y. Meng, The sign problem in quantum monte carlo simulations, in Encyclopedia of Condensed Matter Physics (Elsevier, 2024) p. 879–893.
- C. T. Hann, E. Huffman, and S. Chandrasekharan, Solution to the sign problem in a frustrated quantum impurity model, Annals of Physics 376, 63 (2017).
- R. Mondaini, S. Tarat, and R. T. Scalettar, Quantum critical points and the sign problem, Science 375, 418 (2022).
- E. Ye and N. F. G. Loureiro, Quantum-inspired method for solving the Vlasov-Poisson equations, Phys. Rev. E 106, 035208 (2022).
- Y. Kaga, P. Werner, and S. Hoshino, Eliashberg theory of the jahn-teller-hubbard model, Physical Review B 105, 214516 (2022).
- I. Oseledets, Approximation of matrices with logarithmic number of parameters, in Doklady Mathematics, Vol. 80 (Springer, 2009) pp. 653–654.
- B. N. Khoromskij, O (d log n)-quantics approximation of n-d tensors in high-dimensional numerical modeling, Constructive Approximation 34, 257 (2011).
- H. Takahashi, R. Sakurai, and H. Shinaoka, Compactness of quantics tensor train representations of local imaginary-time propagators (2024), arXiv:2403.09161 [cond-mat.str-el] .
- See Supplemental Material at URL-will-be-inserted-by-publisher for the numerical details of our simulations.
- We must include the factor β2superscript𝛽2\beta^{2}italic_β start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT due to changing variables: x′=τ′/βsuperscript𝑥′superscript𝜏′𝛽x^{\prime}=\tau^{\prime}/\betaitalic_x start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT = italic_τ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT / italic_β and x′′=τ′′/βsuperscript𝑥′′superscript𝜏′′𝛽x^{\prime\prime}=\tau^{\prime\prime}/\betaitalic_x start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT = italic_τ start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT / italic_β.
- J. Kaye, K. Chen, and O. Parcollet, Discrete lehmann representation of imaginary time green’s functions, Phys. Rev. B Condens. Matter 105, 235115 (2022).
- J. Kaye, H. U. R. Strand, and D. Golež, Decomposing imaginary time feynman diagrams using separable basis functions: Anderson impurity model strong coupling expansion (2023), arXiv:2307.08566 [cond-mat.str-el] .
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