Husimi distribution and phase-space analysis of a vibron-model quantum phase transition

TL;DR

This paper uses the Husimi distribution to analyze quantum phase transitions in a vibron model, revealing sharp signatures and proposing new phase transition indicators based on phase-space methods.

Contribution

It introduces phase-space analysis of vibron-model quantum phase transitions using Husimi distribution, inverse participation ratio, and Wehrl's entropy, with a variational approach and zeros characterization.

Findings

Sharp signatures of phase transition via Wehrl's entropy

Minimum Wehrl entropy in the linear phase consistent with a conjecture

Zeros of Husimi distribution as phase transition indicators

Abstract

The Husimi distribution is proposed for a phase space analysis of quantum phase transitions in the two-dimensional $U(3)$ vibron model for $N$-size molecules. We show that the inverse participation ratio and Wehrl's entropy of the Husimi distribution give sharp signatures of the quantum (shape) phase transition from linear to bent. Numerical results are complemented with a variational approach using parity-symmetry-adapted $U(3)$ coherent states, which reach the minimum Wehrl entropy $\frac{N(3+2N)}{(N+1)(N+2)}$, in the rigidly linear phase, according to a generalized Wehrl-Lieb conjecture. We also propose a characterization of the vibron-model quantum phase transition by means of the zeros of the Husimi distribution.