Bridging the gap between topological non-Hermitian physics and open quantum systems

TL;DR

This paper develops a formalism connecting topological properties of non-Hermitian systems with observables in open quantum systems using the Keldysh path-integral approach, enabling detection of topological phase transitions through response measurements.

Contribution

It introduces a frequency-dependent topological index derived from Keldysh Green's functions, linking topological phases to measurable responses in open quantum systems.

Findings

Topological index expressed via Keldysh Green's functions.

Method to detect topological phase transitions through local perturbation responses.

Application demonstrated on a 1D Hatano-Nelson model, highlighting bosonic and fermionic differences.

Abstract

We relate topological properties of non-Hermitian systems and observables of quantum open systems by using the Keldysh path-integral method. We express Keldysh Green's functions in terms of effective non-Hermitian Hamiltonians that contain all the relevant topological information. We arrive at a frequency dependent topological index that is linked to the response of the system to perturbations at a given frequency. We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases