Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I
Abstract In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2019)017 |
| _version_ | 1817989516763332608 |
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| author | Jiaqi Lou Ce Shen Ling-Yan Hung |
| author_facet | Jiaqi Lou Ce Shen Ling-Yan Hung |
| author_sort | Jiaqi Lou |
| collection | DOAJ |
| description | Abstract In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons. |
| first_indexed | 2024-04-14T00:47:55Z |
| format | Article |
| id | doaj.art-6dcf40c1ec354156ba1c3a50e6349c67 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-14T00:47:55Z |
| publishDate | 2019-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-6dcf40c1ec354156ba1c3a50e6349c672022-12-22T02:21:55ZengSpringerOpenJournal of High Energy Physics1029-84792019-04-012019413410.1007/JHEP04(2019)017Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part IJiaqi Lou0Ce Shen1Ling-Yan Hung2Department of Physics and Center for Field Theory and Particle Physics, Fudan UniversityDepartment of Physics and Center for Field Theory and Particle Physics, Fudan UniversityState Key Laboratory of Surface Physics, Fudan UniversityAbstract In this paper, we study gapped edges/interfaces in a 2+1 dimensional bosonic topological order and investigate how the topological entanglement entropy is sensitive to them. We present a detailed analysis of the Ishibashi states describing these edges/interfaces making use of the physics of anyon condensation in the context of Abelian Chern-Simons theory, which is then generalized to more non-Abelian theories whose edge RCFTs are known. Then we apply these results to computing the entanglement entropy of different topological orders. We consider cases where the system resides on a cylinder with gapped boundaries and that the entanglement cut is parallel to the boundary. We also consider cases where the entanglement cut coincides with the interface on a cylinder. In either cases, we find that the topological entanglement entropy is determined by the anyon condensation pattern that characterizes the interface/boundary. We note that conditions are imposed on some non-universal parameters in the edge theory to ensure existence of the conformal interface, analogous to requiring rational ratios of radii of compact bosons.http://link.springer.com/article/10.1007/JHEP04(2019)017AnyonsChern-Simons TheoriesConformal Field Theory |
| spellingShingle | Jiaqi Lou Ce Shen Ling-Yan Hung Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I Journal of High Energy Physics Anyons Chern-Simons Theories Conformal Field Theory |
| title | Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I |
| title_full | Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I |
| title_fullStr | Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I |
| title_full_unstemmed | Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I |
| title_short | Ishibashi states, topological orders with boundaries and topological entanglement entropy. Part I |
| title_sort | ishibashi states topological orders with boundaries and topological entanglement entropy part i |
| topic | Anyons Chern-Simons Theories Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP04(2019)017 |
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