Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model

TL;DR

This paper investigates how the Dicke model's quantum phase transition induces a shift from quasi-integrability to chaos, linking it to a localization-delocalization transition and classical analogues.

Contribution

It provides an exact solution for the Dicke model at the thermodynamic limit and connects quantum chaos onset to a macroscopic superposition formation.

Findings

Quantum chaos appears at the phase transition.

Exact solution relates chaos to superposition.

Classical analogues of the quantum behavior are described.

Abstract

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localisation-delocalisation transition in which a macroscopic superposition is generated. We also describe the classical analogues of this behaviour.