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

TL;DR

This paper introduces a novel method combining global search and Quantics Tensor Train representations to efficiently identify low-rank structures in Feynman diagrams for multiorbital electron-phonon models, overcoming previous computational challenges.

Contribution

It presents a new algorithm that resolves ergodicity issues in tensor-based Feynman diagram analysis, enabling exponential resolution and faster convergence.

Findings

Achieves exponential resolution in time for numerical integration.

Demonstrates faster-than-power-law convergence of error.

Effectively uncovers low-rank structures in complex diagrams.

Abstract

Feynman diagrams are an essential tool for simulating strongly correlated electron systems. However, stochastic quantum Monte Carlo sampling suffers from the sign problem, particularly when solving a multiorbital quantum impurity model. Recently, two approaches have been proposed for efficient numerical treatment of Feynman diagrams: Tensor Cross Interpolation (TCI) to replace stochastic sampling and the Quantics Tensor Train (QTT) representation for compressing space-time dependence. One of the remaining challenges is the nontrivial task of identifying low-rank structures in weak-coupling Feynman diagrams for multiorbital electron-phonon systems. In particular, the traditional TCI algorithm faces an ergodicity problem, which prevents it from fully exploring the multiorbital space. To address this, we incorporate a new algorithm called global search, which resolves this issue. By combining this approach with QTT, we uncover low-rank structures and achieve efficient numerical integration with exponential resolution in time and faster-than-power-law convergence of error relative to computational cost. Additionally, our approach does not require the division of discontinuous regions necessary in non-quantics TCI.