Sensitivity to perturbations and quantum phase transitions

TL;DR

This paper investigates how local density of states and fidelity amplitude reveal the transition from integrability to chaos in the Dicke model, but do not show signs of the quantum phase transition.

Contribution

It demonstrates that local density of states can detect chaos transition but not quantum phase transition in the Dicke Hamiltonian.

Findings

Width of local density of states indicates transition to chaos.

No observable trace of quantum phase transition in these measures.

Fidelity amplitude decay relates to the chaos transition.

Abstract

The local density of states or its Fourier transform, usually called fidelity amplitude, are important measures of quantum irreversibility due to imperfect evolution. In this Rapid Communication we study both quantities in a paradigmatic many body system, the Dicke Hamiltonian, where a single-mode bosonic field interacts with an ensemble of N two-level atoms. This model exhibits a quantum phase transition in the thermodynamic limit, while for finite instances the system undergoes a transition from quasi-integrability to quantum chaotic. We show that the width of the local density of states clearly points out the imprints of the transition from integrability to chaos but no trace remains of the quantum phase transition. The connection with the decay of the fidelity amplitude is also established.