Gauge Invariance and the Quantum Metric Tensor

TL;DR

This paper demonstrates that the quantum metric tensor depends on the gauge choice in quantum systems and introduces a gauge-invariant version, challenging previous assumptions of gauge independence.

Contribution

It explicitly shows gauge dependence of the quantum metric tensor and proposes a new gauge-invariant tensor for the Landau problem.

Findings

Quantum metric tensor depends on gauge choice.

A gauge-invariant quantum metric tensor is constructed.

Implications for understanding quantum phase transitions.

Abstract

The quantum metric tensor was introduced for defining the distance in the parameter space of a system. However, it is also useful for other purposes, like predicting quantum phase transitions. Due to the physical information this tensor provides, its gauge independence sounds reasonable. More over, its original construction was made by looking for this gauge independence. The aim of this paper, however, is to prove that the quantum metric tensor does depend on the gauge. In addition, a real gauge invariant quantum metric tensor is introduced. In this paper, the gauge dependence is explicitly shown by computing the quantum metric tensor of the Landau problem in different gauges. Then, a real gauge independent metric tensor is proposed and computed for the same Landau problem. Since the gauge dependence has not been observed before, the results of this paper might lead to a new study of topics that were believed to be completely understood.