Semi-group influence matrices for non-equilibrium quantum impurity models

TL;DR

This paper presents a new semi-group influence matrix framework for accurately simulating the real-time dynamics of non-equilibrium quantum impurity models, overcoming previous limitations and enabling high-resolution spectral analysis.

Contribution

Introduction of a semi-group influence matrix approach using matrix-product states for improved long-time accuracy in quantum impurity dynamics.

Findings

High-resolution spectral functions for the single impurity Anderson model.

Relaxation rates of impurities after quantum quenches.

Observation of Kondo physics emergence at large loss rates.

Abstract

We introduce a framework for describing the real-time dynamics of quantum impurity models out of equilibrium which is based on the influence matrix approach. By replacing the dynamical map of a large fermionic quantum environment with an effective semi-group influence matrix (SGIM) which acts on a reduced auxiliary space, we overcome the limitations of previous proposals, achieving high accuracy at long evolution times. This SGIM corresponds to a uniform matrix-product state representation of the influence matrix and can be obtained by an efficient algorithm presented in this paper. We benchmark this approach by computing the spectral function of the single impurity Anderson model with high resolution. Further, the spectrum of the effective dynamical map allows us to obtain relaxation rates of the impurity towards equilibrium following a quantum quench. Finally, for a quantum impurity model with on-site two-fermion loss, we compute the spectral function and confirm the emergence of Kondo physics at large loss rates.