Low-rank quantics tensor train representations of Feynman diagrams for multiorbital electron-phonon models
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.
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- 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.
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