Level statistics of a pseudo-Hermitian Dicke model

TL;DR

This paper investigates the spectral properties of a pseudo-Hermitian Dicke model, revealing a transition from Poisson to Wigner level-spacing distributions across quantum phase transitions, challenging previous assumptions.

Contribution

It introduces the study of level statistics in a pseudo-Hermitian Dicke model and shows the relation between quantum phase transitions and changes in spectral statistics.

Findings

Level-spacing distribution is Poisson near integrable limit.

Level-spacing distribution becomes Wigner in non-integrable regimes.

QPT does not always precede changes in level statistics.

Abstract

A non-Hermitian operator that is related to its adjoint through a similarity transformation is defined as a pseudo-Hermitian operator. We study the level-statistics of a pseudo-Hermitian Dicke Hamiltonian that undergoes Quantum Phase Transition (QPT). We find that the level-spacing distribution of this Hamiltonian near the integrable limit is close to Poisson distribution, while it is Wigner distribution for the ranges of the parameters for which the Hamiltonian is non-integrable. We show that the assertion in the context of the standard Dicke model that QPT is a precursor to a change in the level statistics is not valid in general.