Husimi distribution and phase space analysis of Dicke model quantum phase transition

TL;DR

This paper introduces a phase space analysis of the Dicke model's quantum phase transition using the Husimi distribution, revealing sharp signatures through inverse participation ratio and Wehrl entropy, and proposing a new characterization via distribution zeros.

Contribution

It presents a novel phase space approach with Husimi distribution analysis, including a new method based on zeros for characterizing the quantum phase transition in the Dicke model.

Findings

Husimi distribution signatures sharply indicate the phase transition

Inverse participation ratio and Wehrl entropy effectively detect the transition

Zeros of the Husimi distribution provide a new characterization method

Abstract

The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the Dicke model of spin-boson interactions. We show that the inverse participation ratio and Wehrl entropy of the Husimi distribution give sharp signatures of the quantum phase transition. The analysis has been done using two frameworks: a numerical treatment and an analytical variational approximation. Additionally we have proposed a new characterization of the Dicke model quantum phase transition by means of the zeros of the Husimi distribution in the variational approach.