Verlinde formula from entanglement
We derive the Verlinde formula from a recently advocated set of axioms about entanglement entropy [Shi, Kato, and Kim, Ann. Phys., 168164 (2020)10.1016/j.aop.2020.168164]. For any state that obeys these axioms, we can define a quantity that can be identified as the topological S matrix of an abstrac...
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.023132 |
| _version_ | 1797211448220319744 |
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| author | Bowen Shi |
| author_facet | Bowen Shi |
| author_sort | Bowen Shi |
| collection | DOAJ |
| description | We derive the Verlinde formula from a recently advocated set of axioms about entanglement entropy [Shi, Kato, and Kim, Ann. Phys., 168164 (2020)10.1016/j.aop.2020.168164]. For any state that obeys these axioms, we can define a quantity that can be identified as the topological S matrix of an abstract anyon theory. We show that the S matrix is unitary and that it recovers the fusion multiplicities of the underlying anyon theory through the Verlinde formula. Importantly, we rigorously prove the modularity of the theory, which further implies that the mutual braiding statistics of anyons are nontrivial. The key to the proof is a generalized quantum state merging technique, which generates a topology beyond that of any subsystem of the original physical system. |
| first_indexed | 2024-04-24T10:26:39Z |
| format | Article |
| id | doaj.art-0c6755bc2d884f20b8f6283ba24d290e |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:26:39Z |
| publishDate | 2020-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-0c6755bc2d884f20b8f6283ba24d290e2024-04-12T16:53:34ZengAmerican Physical SocietyPhysical Review Research2643-15642020-05-012202313210.1103/PhysRevResearch.2.023132Verlinde formula from entanglementBowen ShiWe derive the Verlinde formula from a recently advocated set of axioms about entanglement entropy [Shi, Kato, and Kim, Ann. Phys., 168164 (2020)10.1016/j.aop.2020.168164]. For any state that obeys these axioms, we can define a quantity that can be identified as the topological S matrix of an abstract anyon theory. We show that the S matrix is unitary and that it recovers the fusion multiplicities of the underlying anyon theory through the Verlinde formula. Importantly, we rigorously prove the modularity of the theory, which further implies that the mutual braiding statistics of anyons are nontrivial. The key to the proof is a generalized quantum state merging technique, which generates a topology beyond that of any subsystem of the original physical system.http://doi.org/10.1103/PhysRevResearch.2.023132 |
| spellingShingle | Bowen Shi Verlinde formula from entanglement Physical Review Research |
| title | Verlinde formula from entanglement |
| title_full | Verlinde formula from entanglement |
| title_fullStr | Verlinde formula from entanglement |
| title_full_unstemmed | Verlinde formula from entanglement |
| title_short | Verlinde formula from entanglement |
| title_sort | verlinde formula from entanglement |
| url | http://doi.org/10.1103/PhysRevResearch.2.023132 |
| work_keys_str_mv | AT bowenshi verlindeformulafromentanglement |