Reflected entropy and Markov gap in Lifshitz theories
Abstract We study the reflected entropy in (1+1)-dimensional Lifshitz field theory whose groundstate is described by a quantum mechanical model. Starting from tripartite Lifshitz groundstates, both critical and gapped, we derive explicit formulas for the Rényi reflected entropies reduced to two adja...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2023)160 |
| _version_ | 1797371207196082176 |
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| author | Clément Berthiere Bin Chen Hongjie Chen |
| author_facet | Clément Berthiere Bin Chen Hongjie Chen |
| author_sort | Clément Berthiere |
| collection | DOAJ |
| description | Abstract We study the reflected entropy in (1+1)-dimensional Lifshitz field theory whose groundstate is described by a quantum mechanical model. Starting from tripartite Lifshitz groundstates, both critical and gapped, we derive explicit formulas for the Rényi reflected entropies reduced to two adjacent or disjoint intervals, directly in the continuum. We show that the reflected entropy in Lifshitz theory does not satisfy monotonicity, in contrast to what is observed for free relativistic fields. We analytically compute the full reflected entanglement spectrum for two disjoint intervals, finding a discrete set of eigenvalues which is that of a thermal density matrix. Furthermore, we investigate the Markov gap, defined as the difference between reflected entropy and mutual information, and find it to be universal and nonvanishing, signaling irreducible tripartite entanglement in Lifshitz groundstates. We also obtain analytical results for the reflected entropies and the Markov gap in 2 + 1 dimensions. Finally, as a byproduct of our results on reflected entropy, we provide exact formulas for two other entanglement-related quantities, namely the computable cross-norm negativity and the operator entanglement entropy. |
| first_indexed | 2024-03-08T18:16:33Z |
| format | Article |
| id | doaj.art-59ee048dc49147ad943b89e78a913d36 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:16:33Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-59ee048dc49147ad943b89e78a913d362023-12-31T12:08:27ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023913510.1007/JHEP09(2023)160Reflected entropy and Markov gap in Lifshitz theoriesClément Berthiere0Bin Chen1Hongjie Chen2Département de Physique, Université de MontréalSchool of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking UniversitySchool of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking UniversityAbstract We study the reflected entropy in (1+1)-dimensional Lifshitz field theory whose groundstate is described by a quantum mechanical model. Starting from tripartite Lifshitz groundstates, both critical and gapped, we derive explicit formulas for the Rényi reflected entropies reduced to two adjacent or disjoint intervals, directly in the continuum. We show that the reflected entropy in Lifshitz theory does not satisfy monotonicity, in contrast to what is observed for free relativistic fields. We analytically compute the full reflected entanglement spectrum for two disjoint intervals, finding a discrete set of eigenvalues which is that of a thermal density matrix. Furthermore, we investigate the Markov gap, defined as the difference between reflected entropy and mutual information, and find it to be universal and nonvanishing, signaling irreducible tripartite entanglement in Lifshitz groundstates. We also obtain analytical results for the reflected entropies and the Markov gap in 2 + 1 dimensions. Finally, as a byproduct of our results on reflected entropy, we provide exact formulas for two other entanglement-related quantities, namely the computable cross-norm negativity and the operator entanglement entropy.https://doi.org/10.1007/JHEP09(2023)160Field Theories in Lower DimensionsField Theories in Higher Dimensions |
| spellingShingle | Clément Berthiere Bin Chen Hongjie Chen Reflected entropy and Markov gap in Lifshitz theories Journal of High Energy Physics Field Theories in Lower Dimensions Field Theories in Higher Dimensions |
| title | Reflected entropy and Markov gap in Lifshitz theories |
| title_full | Reflected entropy and Markov gap in Lifshitz theories |
| title_fullStr | Reflected entropy and Markov gap in Lifshitz theories |
| title_full_unstemmed | Reflected entropy and Markov gap in Lifshitz theories |
| title_short | Reflected entropy and Markov gap in Lifshitz theories |
| title_sort | reflected entropy and markov gap in lifshitz theories |
| topic | Field Theories in Lower Dimensions Field Theories in Higher Dimensions |
| url | https://doi.org/10.1007/JHEP09(2023)160 |
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