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Quantum Fidelity and Thermal Phase Transitions

Haitao Quan, Los Alamos National Laboratory

(Session 1 : Thursday from 8:15-8:45)

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 that for fixed perturbations, the sensitivity of fidelity at high temperatures (where thermal fluctuations wash out information about the transition) is reduced. From the connection to thermodynamic quantities we propose slight variations to the usual fidelity approach that allow us to overcome these limitations. In all cases we find that fidelity remains a good pre-criterion for testing thermal phase transitions, and we use it to analyze the non-zero temperature phase diagram of the Lipkin-Meshkov-Glick model.