Ward-Takahashi Identity and Gauge-Invariant Response Theory for Open Quantum Systems

TL;DR

This paper develops a gauge-invariant response theory for open quantum systems using Lindbladians, revealing that particle-number conservation isn't required for gauge invariance and identifying associated collective modes.

Contribution

It derives the Ward-Takahashi identity for Lindbladian systems and constructs an observable to test gauge invariance without particle-number conservation.

Findings

Particle-number conservation is not necessary for gauge invariance.

Two-body loss induces diffusive modes in dissipative BCS superconductivity.

An observable for testing gauge invariance in open quantum systems is proposed.

Abstract

We derive the Ward-Takahashi identity and establish the gauge-invariant response theory for open quantum systems described by Lindbladians to show that particle-number conservation is not necessary to satisfy gauge invariance. We construct an observable which can be used to test the gauge invariance in the absence of particle-number conservation. We derive the low-energy collective modes that emerge as a consequence of gauge invariance in open quantum systems, and find that two-body loss induces diffusive modes in dissipative Bardeen-Cooper-Schrieffer (BCS) superconductivity. Possible experimental situations for testing gauge invariance in open quantum systems are also discussed.