2021/05/31 by Michał Białończyk, Fernando Javier Gómez-Ruiz, Adolfo del Campo
Computer Science · Mathematics · Physics and Astronomy · #Classical XY model #Fidelity #Integrable system #Ising model #Limit (mathematics) #Parity (physics) #Quantum Information and Cryptography #Quantum many-body systems #Spin (aerodynamics) #Subspace topology #Theoretical and Computational Physics #Thermal #Thermodynamic limit #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1367-2630/ac23f0
published as New J. Phys. 23, 093033 (2021) · 25 pages, 5 figures, 1 Appendix + 1 Figure. Accepted Version
openalex created_date 2021/05/24 · openalex publication_date 2021/09/01 · arxiv created 2021/09/23 · arxiv updated 2021/09/24 · openalex updated_date 2026/08/05
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.