Entanglement in BF theory. Part I. Essential topological entanglement
Abstract We study the entanglement structure of Abelian topological order described by p-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface operators. We define two appropriate notions of subr...
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| Format: | Article |
| Language: | English |
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2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)106 |
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| author | Jackson R. Fliss Stathis Vitouladitis |
| author_facet | Jackson R. Fliss Stathis Vitouladitis |
| author_sort | Jackson R. Fliss |
| collection | DOAJ |
| description | Abstract We study the entanglement structure of Abelian topological order described by p-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface operators. We define two appropriate notions of subregion operator algebras which are related by a form of electric-magnetic duality. To each subregion algebra we assign an entanglement entropy which we coin essential topological entanglement. This is a refinement to the traditional topological entanglement entropy. It is intrinsic to the theory, inherently finite, positive, and sensitive to more intricate topological features of the state and the entangling region. This paper is the first in a series of papers investigating entanglement and topological order in higher dimensions. |
| format | Article |
| id | doaj-art-83bbaea4dce64732b97a63ee4cc4c56f |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-83bbaea4dce64732b97a63ee4cc4c56f2025-02-09T12:07:15ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025114110.1007/JHEP01(2025)106Entanglement in BF theory. Part I. Essential topological entanglementJackson R. Fliss0Stathis Vitouladitis1Department of Applied Mathematics and Theoretical Physics, University of CambridgeInstitute for Theoretical Physics, University of AmsterdamAbstract We study the entanglement structure of Abelian topological order described by p-form BF theory in arbitrary dimensions. We do so directly in the low-energy topological quantum field theory by considering the algebra of topological surface operators. We define two appropriate notions of subregion operator algebras which are related by a form of electric-magnetic duality. To each subregion algebra we assign an entanglement entropy which we coin essential topological entanglement. This is a refinement to the traditional topological entanglement entropy. It is intrinsic to the theory, inherently finite, positive, and sensitive to more intricate topological features of the state and the entangling region. This paper is the first in a series of papers investigating entanglement and topological order in higher dimensions.https://doi.org/10.1007/JHEP01(2025)106Chern-Simons TheoriesTopological Field TheoriesTopological States of MatterAnyons |
| spellingShingle | Jackson R. Fliss Stathis Vitouladitis Entanglement in BF theory. Part I. Essential topological entanglement Journal of High Energy Physics Chern-Simons Theories Topological Field Theories Topological States of Matter Anyons |
| title | Entanglement in BF theory. Part I. Essential topological entanglement |
| title_full | Entanglement in BF theory. Part I. Essential topological entanglement |
| title_fullStr | Entanglement in BF theory. Part I. Essential topological entanglement |
| title_full_unstemmed | Entanglement in BF theory. Part I. Essential topological entanglement |
| title_short | Entanglement in BF theory. Part I. Essential topological entanglement |
| title_sort | entanglement in bf theory part i essential topological entanglement |
| topic | Chern-Simons Theories Topological Field Theories Topological States of Matter Anyons |
| url | https://doi.org/10.1007/JHEP01(2025)106 |
| work_keys_str_mv | AT jacksonrfliss entanglementinbftheorypartiessentialtopologicalentanglement AT stathisvitouladitis entanglementinbftheorypartiessentialtopologicalentanglement |