Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results

Abstract

We derive the exact expression for the Uhlmann fidelity between arbitrary thermal Gibbs states of the quantum XY model in a transverse field with finite system size. Using it, we conduct a thorough analysis of the fidelity susceptibility of thermal states for the Ising model in a transverse field. We compare the exact results with a common approximation that considers only the positive-parity subspace, which is shown to be valid only at high temperatures. The proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. We show that this enhancement persists in the thermodynamic limit and scales quadratically with the system size. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates, from which simple expressions are obtained for the thermal susceptibility and specific heat.

25 pages, 5 figures, 1 Appendix + 1 Figure. Accepted Version

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Cited by in corpus (3)

• Detection of quantum phase boundary at finite temperatures in integrable spin models
• A universal black-box quantum Monte Carlo approach to quantum phase transitions
• Signature of quantum phase transition manifested in quantum fidelity at finite temperature