Quantum Fidelity and Thermal Phase Transitions

TL;DR

This paper investigates the effectiveness of quantum fidelity in identifying thermal phase transitions, highlighting its strengths and limitations through theoretical analysis and application to the Lipkin-Meshkov-Glick model.

Contribution

It provides a detailed analysis of the fidelity approach for thermal phase transitions, including its applicability, limitations, and practical use in phase diagram analysis.

Findings

Fidelity is more effective for λ transitions with divergent free energy derivatives.

High temperature fluctuations reduce fidelity's sensitivity to phase transitions.

Fidelity can serve as a preliminary criterion for detecting thermal phase transitions.

Abstract

We study the quantum fidelity approach to characterize thermal phase transitions. Specifically, we focus on the mixed-state fidelity induced by a perturbation in temperature. We consider the behavior of fidelity in two types of second-order thermal phase transitions (based on the type of non-analiticity of free energy), and we find that usual fidelity criteria for identifying critical points is more applicable to the case of $\lambda$ transitions (divergent second derivatives of free energy). Our study also reveals limitations of the fidelity approach: sensitivity to high temperature thermal fluctuations that wash out information about the transition, and inability of fidelity to distinguish between crossovers and proper phase transitions. In spite of these limitations, however, we find that fidelity remains a good pre-criterion for testing thermal phase transitions, which we use to analyze the non-zero temperature phase diagram of the Lipkin-Meshkov-Glick model.