Lattice models that realize Z n -1 symmetry-protected topological states for even n
© 2020 American Physical Society. Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high-energy scales while other topological excitations have low energies. The low-energy properties of topological orders in t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society (APS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/136306 |
| _version_ | 1826208821576466432 |
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| author | Tsui, Lokman Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Tsui, Lokman Wen, Xiao-Gang |
| author_sort | Tsui, Lokman |
| collection | MIT |
| description | © 2020 American Physical Society. Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high-energy scales while other topological excitations have low energies. The low-energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry-protected topological order. This motivates us, as a simplest example, to study a lattice model of Zn-1 symmetry-protected topological (1-SPT) states in 3+1 dimensions for even n. We write an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with nontrivial self-statistics. For the n=2 case, where the bulk classification is given by an integer m mod 4, we show that the boundary can be gapped with double-semion topological order for m=1 and toric code for m=2. The bulk ground-state wave-function amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry. |
| first_indexed | 2024-09-23T14:12:51Z |
| format | Article |
| id | mit-1721.1/136306 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:12:51Z |
| publishDate | 2021 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1363062023-12-19T20:58:17Z Lattice models that realize Z n -1 symmetry-protected topological states for even n Tsui, Lokman Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics © 2020 American Physical Society. Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high-energy scales while other topological excitations have low energies. The low-energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry-protected topological order. This motivates us, as a simplest example, to study a lattice model of Zn-1 symmetry-protected topological (1-SPT) states in 3+1 dimensions for even n. We write an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with nontrivial self-statistics. For the n=2 case, where the bulk classification is given by an integer m mod 4, we show that the boundary can be gapped with double-semion topological order for m=1 and toric code for m=2. The bulk ground-state wave-function amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry. 2021-10-27T20:34:48Z 2021-10-27T20:34:48Z 2020 2021-07-09T13:36:30Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136306 en 10.1103/PHYSREVB.101.035101 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. application/pdf American Physical Society (APS) APS |
| spellingShingle | Tsui, Lokman Wen, Xiao-Gang Lattice models that realize Z n -1 symmetry-protected topological states for even n |
| title | Lattice models that realize Z n -1 symmetry-protected topological states for even n |
| title_full | Lattice models that realize Z n -1 symmetry-protected topological states for even n |
| title_fullStr | Lattice models that realize Z n -1 symmetry-protected topological states for even n |
| title_full_unstemmed | Lattice models that realize Z n -1 symmetry-protected topological states for even n |
| title_short | Lattice models that realize Z n -1 symmetry-protected topological states for even n |
| title_sort | lattice models that realize z n 1 symmetry protected topological states for even n |
| url | https://hdl.handle.net/1721.1/136306 |
| work_keys_str_mv | AT tsuilokman latticemodelsthatrealizezn1symmetryprotectedtopologicalstatesforevenn AT wenxiaogang latticemodelsthatrealizezn1symmetryprotectedtopologicalstatesforevenn |