Thermal correction to entanglement spectrum for conformal field theories
Abstract We calculate the thermal correction to the entanglement spectrum for separating a single interval of two dimensional conformal field theories. Our derivation is a direct extension of the thermal correction to the Rényi entropy. Within a low-temperature expansion by including only the first...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP08(2022)239 |
| _version_ | 1811188807722074112 |
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| author | Yin Tang Qicheng Tang W. Zhu |
| author_facet | Yin Tang Qicheng Tang W. Zhu |
| author_sort | Yin Tang |
| collection | DOAJ |
| description | Abstract We calculate the thermal correction to the entanglement spectrum for separating a single interval of two dimensional conformal field theories. Our derivation is a direct extension of the thermal correction to the Rényi entropy. Within a low-temperature expansion by including only the first excited state in the thermal density matrix, we approach analytical results of the thermal correction to the entanglement spectrum at both of the small and large interval limit. We find the temperature correction reduces the large eigenvalues in the entanglement spectrum while increases the small eigenvalues in the entanglement spectrum, leading to an overall crossover changing pattern of the entanglement spectrum. Crucially, at low-temperature limit, the thermal corrections are dominated by the first excited state and depend on its scaling dimension ∆ and degeneracy g. This opens an avenue to extract universal information of underlying conformal data via the thermal entanglement spectrum. All of these analytical computation is supported from numerical simulations using 1+1 dimensional free fermion. Finally, we extend our calculation to resolve the thermal correction to the symmetry-resolved entanglement spectrum. |
| first_indexed | 2024-04-11T14:24:27Z |
| format | Article |
| id | doaj.art-6a14341c80134330818f6b28ac1e1667 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T14:24:27Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-6a14341c80134330818f6b28ac1e16672022-12-22T04:18:55ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022811910.1007/JHEP08(2022)239Thermal correction to entanglement spectrum for conformal field theoriesYin Tang0Qicheng Tang1W. Zhu2Department of Physics, Zhejiang UniversityDepartment of Physics, Zhejiang UniversitySchool of Science, Westlake UniversityAbstract We calculate the thermal correction to the entanglement spectrum for separating a single interval of two dimensional conformal field theories. Our derivation is a direct extension of the thermal correction to the Rényi entropy. Within a low-temperature expansion by including only the first excited state in the thermal density matrix, we approach analytical results of the thermal correction to the entanglement spectrum at both of the small and large interval limit. We find the temperature correction reduces the large eigenvalues in the entanglement spectrum while increases the small eigenvalues in the entanglement spectrum, leading to an overall crossover changing pattern of the entanglement spectrum. Crucially, at low-temperature limit, the thermal corrections are dominated by the first excited state and depend on its scaling dimension ∆ and degeneracy g. This opens an avenue to extract universal information of underlying conformal data via the thermal entanglement spectrum. All of these analytical computation is supported from numerical simulations using 1+1 dimensional free fermion. Finally, we extend our calculation to resolve the thermal correction to the symmetry-resolved entanglement spectrum.https://doi.org/10.1007/JHEP08(2022)239Conformal and W SymmetryField Theories in Lower DimensionsThermal Field Theory |
| spellingShingle | Yin Tang Qicheng Tang W. Zhu Thermal correction to entanglement spectrum for conformal field theories Journal of High Energy Physics Conformal and W Symmetry Field Theories in Lower Dimensions Thermal Field Theory |
| title | Thermal correction to entanglement spectrum for conformal field theories |
| title_full | Thermal correction to entanglement spectrum for conformal field theories |
| title_fullStr | Thermal correction to entanglement spectrum for conformal field theories |
| title_full_unstemmed | Thermal correction to entanglement spectrum for conformal field theories |
| title_short | Thermal correction to entanglement spectrum for conformal field theories |
| title_sort | thermal correction to entanglement spectrum for conformal field theories |
| topic | Conformal and W Symmetry Field Theories in Lower Dimensions Thermal Field Theory |
| url | https://doi.org/10.1007/JHEP08(2022)239 |
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