Bures metric over thermal state manifolds and quantum criticality

TL;DR

This paper investigates how the Bures metric on thermal state manifolds reveals quantum criticality and phase diagram features, including cross-over regions, by analyzing temperature and external field effects.

Contribution

It extends the metric approach to quantum criticality by analyzing the Bures metric's behavior across temperature and external fields, revealing new insights into phase diagrams.

Findings

The Bures metric characterizes quantum critical regions via temperature scaling.

Analysis of the metric tensor with external fields complements phase diagram understanding.

The approach extends the application of metric methods to quantum phase transitions.

Abstract

We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows to complement the understanding of the phase diagram including cross-over regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.