Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions
We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z_{2}-gauge theory with emergent fermionic Kramers doubl...
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/110247 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826212729168330752 |
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| author | Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang |
| author_sort | Wen, Xiao-Gang |
| collection | MIT |
| description | We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z_{2}-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin^{+} structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z_{2} topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z_{2} SET orders have stringlike excitations that carry anomalous (nononsite) Z_{2} symmetry, which can be viewed as a fractionalization of Z_{2} symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory. |
| first_indexed | 2024-09-23T15:36:19Z |
| format | Article |
| id | mit-1721.1/110247 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:36:19Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1102472022-10-02T02:57:47Z Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang We propose a generic construction of exactly soluble local bosonic models that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble bosonic model that realizes a (3+1)-dimensional [(3+1)D] Z_{2}-gauge theory with emergent fermionic Kramers doublet. We show that the emergence of such a fermion will cause the nucleation of certain topological excitations in space-time without pin^{+} structure. The exactly soluble model also leads to a statistical transmutation in (3+1)D. In addition, we construct exactly soluble bosonic models that realize 2 types of time-reversal symmetry-enriched Z_{2} topological orders in 2+1 dimensions, and 20 types of simplest time-reversal symmetry-enriched topological (SET) orders which have only one nontrivial pointlike and stringlike topological excitation. Many physical properties of those topological states are calculated using the exactly soluble models. We find that some time-reversal SET orders have pointlike excitations that carry Kramers doublet, a fractionalized time-reversal symmetry. We also find that some Z_{2} SET orders have stringlike excitations that carry anomalous (nononsite) Z_{2} symmetry, which can be viewed as a fractionalization of Z_{2} symmetry on strings. Our construction is based on cochains and cocycles in algebraic topology, which is very versatile. In principle, it can also realize emergent topological field theory beyond the twisted gauge theory. National Science Foundation (U.S.) (Grant No. DMR-1506475) National Natural Science Foundation of China (Grant No. 11274192) 2017-06-26T12:52:38Z 2017-06-26T12:52:38Z 2017-05 2017-01 2017-06-02T16:41:21Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/110247 Wen, Xiao-Gang. “Exactly Soluble Local Bosonic Cocycle Models, Statistical Transmutation, and Simplest Time-Reversal Symmetric Topological Orders in 3+1 Dimensions.” Physical Review B 95, no. 20 (May 30, 2017). https://orcid.org/0000-0002-5874-581X en http://dx.doi.org/10.1103/PhysRevB.95.205142 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 | Wen, Xiao-Gang Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions |
| title | Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions |
| title_full | Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions |
| title_fullStr | Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions |
| title_full_unstemmed | Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions |
| title_short | Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions |
| title_sort | exactly soluble local bosonic cocycle models statistical transmutation and simplest time reversal symmetric topological orders in 3 1 dimensions |
| url | http://hdl.handle.net/1721.1/110247 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT wenxiaogang exactlysolublelocalbosoniccocyclemodelsstatisticaltransmutationandsimplesttimereversalsymmetrictopologicalordersin31dimensions |