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.
Highlights
Quantum phase transitions (QPTs), unlike classical phase transitions, are induced by quantum fluctuations related to Heisenberg uncertainty and can occur at zero temperature
We provide exact expressions for fidelity between two arbitrary thermal states in the quantum XY models and analyze the temperature dependence of fidelity susceptibility in a paradigmatic test-bed for quantum critical phenomena, the quantum Ising model in a transverse field
We have shown that such an approach fails in the characterization of quantum critical phenomena using the ground-state fidelity and fidelity susceptibility
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Michał Białonczyk1,∗ , Fernando Javier Gomez-Ruiz2,3,4 and Adolfo del Campo2,4,5 Keywords: quantum phase transitions, Uhlmann fidelity, fidelity susceptibility, Ising model, XY model, integrable spin chains, thermal states
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have