Information Geometry and Quantum Phase Transitions in the Dicke Model

TL;DR

This paper investigates the information geometric properties of the Dicke model, revealing that the scalar curvature remains continuous across quantum phase transitions, indicating a smooth parameter manifold.

Contribution

It provides a detailed analysis of the scalar curvature in the Dicke model's parameter space, including the effects of the rotating wave approximation, highlighting the smoothness at phase transitions.

Findings

Scalar curvature is continuous across the phase boundary

Parameter manifold remains smooth at the phase transition

Analysis includes both with and without rotating wave approximation

Abstract

We study information geometry of the Dicke model, in the thermodynamic limit. The scalar curvature $R$ of the Riemannian metric tensor induced on the parameter space of the model is calculated. We analyze this both with and without the rotating wave approximation, and show that the parameter manifold is smooth even at the phase transition, and that the scalar curvature is continuous across the phase boundary.