Hierarchical Liouville-space approach to nonequilibrium dynamical properties of quantum impurity systems

TL;DR

This paper introduces a hierarchical Liouville-space method for accurately computing nonequilibrium dynamical responses of quantum impurity systems, applicable to various physical properties and validated on the Anderson model.

Contribution

It develops a universal hierarchical equations of motion framework combined with linear response theory for quantum impurity systems, enhancing response function calculations.

Findings

Accurately computes spectral density, charge fluctuations, and magnetic susceptibility.

Demonstrates effectiveness on the single-impurity Anderson model.

Results converge with hierarchy truncation, ensuring quantitative reliability.

Abstract

We propose a hierarchical dynamics approach for evaluation of nonequilibrium dynamic response properties of quantum impurity systems. It is based on a hierarchical equations of motion formalism, in conjunction with a linear response theory established in the hierarchical Liouville space. This provides an accurate and universal tool for characterization of arbitrary response and correlation functions of local impurities, as well as transport related response properties. The practicality of our proposed approach is demonstrated via the evaluation of various dynamical properties of a single-impurity Anderson model. These include the impurity spectral density, local charge fluctuation, local magnetic susceptibility, and current-voltage admittance, in both equilibrium and nonequilibrium situations. The numerical results are considered to achieve the quantitative accuracy, as long as they converge with respect to the truncation of the hierarchy.