Memory-Efficient Nonequilibrium Green's Function Framework Built On Quantics Tensor Trains

TL;DR

This paper introduces a memory-efficient framework for nonequilibrium Green's function simulations using quantics tensor trains, enabling high-resolution, long-time studies of complex quantum phenomena.

Contribution

It presents a novel QTT-based approach that significantly reduces memory requirements for simulating nonequilibrium Green's functions in lattice models.

Findings

Enables simulations exceeding standard implementation time limits.

Allows high momentum resolution in nonequilibrium scenarios.

Facilitates studies of transient Floquet physics and thermalization.

Abstract

One of the challenges in diagrammatic simulations of nonequilibrium phenomena in lattice models is the large memory demand for storing momentum-dependent two-time correlation functions. This problem can be overcome with the recently introduced quantics tensor train (QTT) representation of multivariable functions. Here, we demonstrate nonequilibrium Green's function simulations within the $GW$ and Migdal approximations with high momentum resolution, up to times which exceed the capabilities of standard implementations and are long enough to study, e.g., transient Floquet physics during multi-cycle electric field pulses and thermalization dynamics. The self-consistent calculation on the three-leg Kadanoff-Baym contour is fully self-contained, employing only QTT-compressed functions and input functions which are either generated directly in QTT form or obtained via quantics tensor cross interpolation.