Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results
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. W...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2021-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/ac23f0 |
| _version_ | 1797750067519553536 |
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| author | Michał Białończyk Fernando Javier Gómez-Ruiz Adolfo del Campo |
| author_facet | Michał Białończyk Fernando Javier Gómez-Ruiz Adolfo del Campo |
| author_sort | Michał Białończyk |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:27:23Z |
| format | Article |
| id | doaj.art-53f72d77d57642bf86c34aa027b9b820 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:27:23Z |
| publishDate | 2021-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-53f72d77d57642bf86c34aa027b9b8202023-08-08T15:39:08ZengIOP PublishingNew Journal of Physics1367-26302021-01-0123909303310.1088/1367-2630/ac23f0Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact resultsMichał Białończyk0https://orcid.org/0000-0001-6909-6213Fernando Javier Gómez-Ruiz1https://orcid.org/0000-0002-1855-0671Adolfo del Campo2https://orcid.org/0000-0003-2219-2851Institute of Theoretical Physics, Jagiellonian University , Łojasiewicza 11, 30-348 Kraków, PolandDonostia 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, LuxembourgDonostia International Physics Center , E-20018 San Sebastián, Spain; Department of Physics and Materials Science, University of Luxembourg , L-1511 Luxembourg, Luxembourg; Department of Physics, University of Massachusetts , Boston, MA 02125, United States of AmericaWe 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.https://doi.org/10.1088/1367-2630/ac23f0quantum phase transitionsUhlmann fidelityfidelity susceptibilityIsing modelXY modelintegrable spin chains |
| spellingShingle | Michał Białończyk Fernando Javier Gómez-Ruiz Adolfo del Campo Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results New Journal of Physics quantum phase transitions Uhlmann fidelity fidelity susceptibility Ising model XY model integrable spin chains |
| title | Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results |
| title_full | Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results |
| title_fullStr | Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results |
| title_full_unstemmed | Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results |
| title_short | Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results |
| title_sort | uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature exact results |
| topic | quantum phase transitions Uhlmann fidelity fidelity susceptibility Ising model XY model integrable spin chains |
| url | https://doi.org/10.1088/1367-2630/ac23f0 |
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