The Husimi distribution, the Wehrl entropy and the superradiant phase in spin-boson interactions

TL;DR

This paper investigates the quantum phase transition in the Dicke model using the Husimi distribution and Wehrl entropy, revealing phase transition indicators without relying on common approximations.

Contribution

It introduces a novel analysis of the Husimi distribution and Wehrl entropy to characterize the superradiant phase transition in the Dicke model without Holstein-Primakoff approximation.

Findings

Wehrl entropy sharply changes at the critical point.

Zeros of the Husimi distribution characterize the phase transition.

Exact numerical and variational methods confirm these indicators.

Abstract

We study the Husimi distribution of the ground state in the Dicke model of field-matter interactions to visualize the quantum phase transition, from normal to superradiant, in phase-space. We follow an exact numerical and variational analysis, without making use of the usual Holstein-Primakoff approximation. We find that Wehrl entropy of the Husimi distribution provides an indicator of the sharp change of symmetry trough the critical point. Additionally, we note that the zeros of the Husimi distribution characterize the Dicke model quantum phase transition.