Crystalline topological phases as defect networks
A crystalline topological phase is a topological phase with spatial symmetries. In this work, we give a very general physical picture of such phases: A topological phase with spatial symmetry G (with internal symmetry G[subscript int] ≤ G) is described by a defect network, a G-symmetric network of d...
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| Format: | Article |
| Language: | English |
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American Physical Society
2019
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| Online Access: | http://hdl.handle.net/1721.1/120966 |
| _version_ | 1811092570000850944 |
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| author | Thorngren, Ryan Else, Dominic V |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Thorngren, Ryan Else, Dominic V |
| author_sort | Thorngren, Ryan |
| collection | MIT |
| description | A crystalline topological phase is a topological phase with spatial symmetries. In this work, we give a very general physical picture of such phases: A topological phase with spatial symmetry G (with internal symmetry G[subscript int] ≤ G) is described by a defect network, a G-symmetric network of defects in a topological phase with internal symmetry G[subscript int]. The defect network picture works both for symmetry-protected topological (SPT) and symmetry-enriched topological (SET) phases, in systems of either bosons or fermions. We derive this picture both by physical arguments and by a mathematical derivation from the general framework of Thorngren and Else [Phys. Rev. X 8, 011040 (2018)2160-330810.1103/PhysRevX.8.011040]. In the case of crystalline SPT phases, the defect network picture reduces to a previously studied dimensional reduction picture, thus establishing the equivalence of this picture with the general framework of Thorngren and Else applied to crystalline SPTs. |
| first_indexed | 2024-09-23T15:20:18Z |
| format | Article |
| id | mit-1721.1/120966 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:20:18Z |
| publishDate | 2019 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1209662022-10-02T02:19:07Z Crystalline topological phases as defect networks Thorngren, Ryan Else, Dominic V Massachusetts Institute of Technology. Department of Physics Else, Dominic V A crystalline topological phase is a topological phase with spatial symmetries. In this work, we give a very general physical picture of such phases: A topological phase with spatial symmetry G (with internal symmetry G[subscript int] ≤ G) is described by a defect network, a G-symmetric network of defects in a topological phase with internal symmetry G[subscript int]. The defect network picture works both for symmetry-protected topological (SPT) and symmetry-enriched topological (SET) phases, in systems of either bosons or fermions. We derive this picture both by physical arguments and by a mathematical derivation from the general framework of Thorngren and Else [Phys. Rev. X 8, 011040 (2018)2160-330810.1103/PhysRevX.8.011040]. In the case of crystalline SPT phases, the defect network picture reduces to a previously studied dimensional reduction picture, thus establishing the equivalence of this picture with the general framework of Thorngren and Else applied to crystalline SPTs. 2019-03-14T19:00:10Z 2019-03-14T19:00:10Z 2019-03 2018-11 2019-03-14T18:00:27Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/120966 Else, Dominic V. and Ryan Thorngren. "Crystalline topological phases as defect networks." Physical Review B 99, 11 (March 2019): 115116 © 2019 American Physical Society en http://dx.doi.org/10.1103/PhysRevB.99.115116 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Thorngren, Ryan Else, Dominic V Crystalline topological phases as defect networks |
| title | Crystalline topological phases as defect networks |
| title_full | Crystalline topological phases as defect networks |
| title_fullStr | Crystalline topological phases as defect networks |
| title_full_unstemmed | Crystalline topological phases as defect networks |
| title_short | Crystalline topological phases as defect networks |
| title_sort | crystalline topological phases as defect networks |
| url | http://hdl.handle.net/1721.1/120966 |
| work_keys_str_mv | AT thorngrenryan crystallinetopologicalphasesasdefectnetworks AT elsedominicv crystallinetopologicalphasesasdefectnetworks |