Nonequilibrium diagrammatic many-body simulations with quantics tensor trains

TL;DR

This paper demonstrates that using quantics tensor train representations significantly improves the efficiency of nonequilibrium Green's function simulations for the 2D Hubbard model, reducing computational cost and memory usage without sacrificing accuracy.

Contribution

The authors implement a tensor train approach to compress nonequilibrium Green's functions, enabling more efficient simulations of the Hubbard model at long times.

Findings

Tensor train compression maintains accuracy in simulations.

Significant reduction in computational effort and memory usage.

Enhanced scaling with time contour length.

Abstract

The nonequilibrium Green's function formalism provides a versatile and powerful framework for numerical studies of nonequilibrium phenomena in correlated many-body systems. For calculations starting from an equilibrium initial state, a standard approach consists of discretizing the Kadanoff-Baym contour and implementing a causal time-stepping scheme in which the self-energy of the system plays the role of a memory kernel. This approach becomes computationally expensive at long times, because of the convolution integrals and the large amount of computer memory needed to store the Green's functions. A recent idea for the compression of nonequilibrium Green's functions is the quantics tensor train representation. Here, we explore this approach by implementing equilibrium and nonequilibrium simulations of the two-dimensional Hubbard model with a second-order weak-coupling approximation to the self-energy. We show that calculations with compressed two-time functions are possible without any loss of accuracy, and that the quantics tensor train implementation shows a much improved scaling of the computational effort and memory demand with the length of the time contour.