Truncating the memory time in nonequilibrium DMFT calculations

TL;DR

This paper introduces truncation schemes for the memory kernel in nonequilibrium DMFT, significantly reducing computational costs and enabling longer time simulations of strongly correlated systems.

Contribution

The study systematically investigates memory time truncation in nonequilibrium DMFT, demonstrating that it maintains accuracy while enabling longer simulations.

Findings

Effective truncation schemes preserve accuracy.

Reduced computational cost allows longer time evolution.

Enables study of prethermalization and thermalization processes.

Abstract

The nonequilibrium Green's functions (NEGF) approach is a versatile theoretical tool, which allows to describe the electronic structure, spectroscopy and dynamics of strongly correlated systems. The applicability of this method is, however, limited by its considerable computational cost. Due to the treatment of the full two-time dependence of the NEGF the underlying equations of motion involve a long-lasting non-Markovian memory kernel that results in at least a $N^3_t$ scaling in the number of time points $N_t$. The system's memory time is, however, reduced in the presence of a thermalizing bath. In particular, dynamical mean-field theory (DMFT) -- one of the most successful approaches to strongly correlated lattice systems - maps extended systems to an effective impurity coupled to a bath. In this work, we systematically investigate how the memory time can be truncated in nonequilibrium DMFT simulations of the Hubbard and Hubbard-Holstein model. We show that suitable truncation schemes, which substantially reduce the computational cost, result in excellent approximations to the full time evolution. This approach enables the propagation to longer times, making fundamental processes like prethermalization and the final stages of thermalization accessible to nonequilibrium DMFT.