Quantum chaos and operator fidelity metric

TL;DR

This paper proposes using the operator fidelity metric as an information-theoretic tool to identify the transition from regular to chaotic quantum behavior, supported by random matrix theory and numerical analysis of the Dicke model.

Contribution

It introduces the operator fidelity metric as a new order parameter for detecting quantum chaos and demonstrates its effectiveness through theoretical conjecture and numerical evidence.

Findings

Operator fidelity metric distinguishes regular from chaotic quantum phases.

Random matrix theory supports the metric as an order parameter.

Numerical results in the Dicke model confirm the conjecture.

Abstract

We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. We use random matrix theory arguments to conjecture that the operator fidelity metric can be used as an "order parameter" to discriminates phases with regular behaviour from quantum chaotic ones. A numerical study of the onset of chaotic in the Dicke model is given in order to support the conjecture