Reference : Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite tem...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Physics
Physics and Materials Science
Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results
Białończyk, Michał [Institute of Theoretical Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Krak´ow, Poland]
Gomez-Ruiz, Fernando Javier [Donostia International Physics Center, E-20018 San Sebastián, Spain > > > ; Departamento de Física, Universidad de los Andes, A.A. 4976, Bogotá D. C., Colombia > > > ; Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg]
Del Campo Echevarria, Adolfo mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS) >]
New Journal of Physics
[en] 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.

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