Non-local order parameters and quantum entanglement for fermionic topological field theories
Abstract We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological quantum field theories (TQFTs). By formulat...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)121 |
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| author | Kansei Inamura Ryohei Kobayashi Shinsei Ryu |
| author_facet | Kansei Inamura Ryohei Kobayashi Shinsei Ryu |
| author_sort | Kansei Inamura |
| collection | DOAJ |
| description | Abstract We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological quantum field theories (TQFTs). By formulating the order parameters in the Hilbert space of state sum TQFT, we establish the connection between the quantized non-local order parameters and the underlying field theory, clarifying the nature of the order parameters as topological invariants. We also formulate several entanglement measures including the entanglement negativity on state sum spin TQFT, and describe the exact correspondence of the entanglement measures to path integrals on a closed surface equipped with a specific spin structure. |
| format | Article |
| id | doaj-art-71ad9a2b89ab4055a4bff0acf859c347 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-71ad9a2b89ab4055a4bff0acf859c3472025-01-26T12:11:22ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020113110.1007/JHEP01(2020)121Non-local order parameters and quantum entanglement for fermionic topological field theoriesKansei Inamura0Ryohei Kobayashi1Shinsei Ryu2Institute for Solid State Physics, University of TokyoInstitute for Solid State Physics, University of TokyoJames Franck Institute and Kadanoff Center for Theoretical Physics, University of ChicagoAbstract We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological quantum field theories (TQFTs). By formulating the order parameters in the Hilbert space of state sum TQFT, we establish the connection between the quantized non-local order parameters and the underlying field theory, clarifying the nature of the order parameters as topological invariants. We also formulate several entanglement measures including the entanglement negativity on state sum spin TQFT, and describe the exact correspondence of the entanglement measures to path integrals on a closed surface equipped with a specific spin structure.https://doi.org/10.1007/JHEP01(2020)121Topological Field TheoriesTopological States of Matter |
| spellingShingle | Kansei Inamura Ryohei Kobayashi Shinsei Ryu Non-local order parameters and quantum entanglement for fermionic topological field theories Journal of High Energy Physics Topological Field Theories Topological States of Matter |
| title | Non-local order parameters and quantum entanglement for fermionic topological field theories |
| title_full | Non-local order parameters and quantum entanglement for fermionic topological field theories |
| title_fullStr | Non-local order parameters and quantum entanglement for fermionic topological field theories |
| title_full_unstemmed | Non-local order parameters and quantum entanglement for fermionic topological field theories |
| title_short | Non-local order parameters and quantum entanglement for fermionic topological field theories |
| title_sort | non local order parameters and quantum entanglement for fermionic topological field theories |
| topic | Topological Field Theories Topological States of Matter |
| url | https://doi.org/10.1007/JHEP01(2020)121 |
| work_keys_str_mv | AT kanseiinamura nonlocalorderparametersandquantumentanglementforfermionictopologicalfieldtheories AT ryoheikobayashi nonlocalorderparametersandquantumentanglementforfermionictopologicalfieldtheories AT shinseiryu nonlocalorderparametersandquantumentanglementforfermionictopologicalfieldtheories |