Efficient Time-Domain Approach for Linear Response Functions

TL;DR

This paper introduces a highly efficient time-domain method for calculating linear response functions, improving computational performance significantly and applicable to complex quantum systems like topological insulators.

Contribution

It presents a novel time-domain approach for linear response functions based on the time evolution of displacement operators, with substantial efficiency gains.

Findings

Achieved at least 1000-fold performance improvement in quantum resistivity calculations.

Successfully applied the method to analyze electrical conductivity and topological states.

Connected the approach to the fluctuation-dissipation theorem.

Abstract

We derive the general Kubo formula in a form that solely utilizes the time evolution of displacement operators. The derivation is based on the decomposition of the linear response function into its time symmetric and time anti-symmetric part. We relate this form to the well-known fluctuation-dissipation formula and discuss theoretical and numerical aspects of it. The approach is illustrated with an analytical example for magnetic resonance as well as a numerical example where we analyze the electrical conductivity tensor and the Chern insulating state of the disordered Haldane model. We introduce a highly efficient time-domain approach that describes the quantum dynamics of the resistivity of this model with an at least 1000-fold better performance in comparison to existing time-evolution schemes.