Simple-current algebra constructions of 2+1-dimensional topological orders
Self-consistent (non-)Abelian statistics in 2+1 dimensions (2+1D) are classified by modular tensor categories (MTCs). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients N[ij over k] and spins s_{i}, was proposed. A numerical search based on these axioms led to a l...
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| Format: | Article |
| Language: | English |
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American Physical Society
2016
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| Online Access: | http://hdl.handle.net/1721.1/100805 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1811076947027951616 |
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| author | Schoutens, Kareljan Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Schoutens, Kareljan Wen, Xiao-Gang |
| author_sort | Schoutens, Kareljan |
| collection | MIT |
| description | Self-consistent (non-)Abelian statistics in 2+1 dimensions (2+1D) are classified by modular tensor categories (MTCs). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients N[ij over k] and spins s_{i}, was proposed. A numerical search based on these axioms led to a list of possible (non-)Abelian statistics, with rank up to N = 7. However, there is no guarantee that all solutions to the simplified axioms are consistent and can be realized by bosonic physical systems. In this paper, we use simple-current algebra to address this issue. We explicitly construct many-body wave functions, aiming to realize the entries in the list (i.e., realize their fusion coefficients N[ij over k] and spins s[subscript i]). We find that all entries can be constructed by simple-current algebra plus conjugation under time-reversal symmetry. This supports the conjecture that simple-current algebra is a general approach that allows us to construct all (non-)Abelian statistics in 2+1D. It also suggests that the simplified theory based on (N[ij over k], s[subscript i]) is a classifying theory at least for simple bosonic 2+1D topological orders (up to invertible topological orders). |
| first_indexed | 2024-09-23T10:31:37Z |
| format | Article |
| id | mit-1721.1/100805 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:31:37Z |
| publishDate | 2016 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1008052022-09-27T09:55:10Z Simple-current algebra constructions of 2+1-dimensional topological orders Schoutens, Kareljan Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Self-consistent (non-)Abelian statistics in 2+1 dimensions (2+1D) are classified by modular tensor categories (MTCs). In recent works, a simplified axiomatic approach to MTCs, based on fusion coefficients N[ij over k] and spins s_{i}, was proposed. A numerical search based on these axioms led to a list of possible (non-)Abelian statistics, with rank up to N = 7. However, there is no guarantee that all solutions to the simplified axioms are consistent and can be realized by bosonic physical systems. In this paper, we use simple-current algebra to address this issue. We explicitly construct many-body wave functions, aiming to realize the entries in the list (i.e., realize their fusion coefficients N[ij over k] and spins s[subscript i]). We find that all entries can be constructed by simple-current algebra plus conjugation under time-reversal symmetry. This supports the conjecture that simple-current algebra is a general approach that allows us to construct all (non-)Abelian statistics in 2+1D. It also suggests that the simplified theory based on (N[ij over k], s[subscript i]) is a classifying theory at least for simple bosonic 2+1D topological orders (up to invertible topological orders). National Science Foundation (U.S.) (Grant DMR-1005541) National Natural Science Foundation (China) (11274192) Templeton Foundation (39901) 2016-01-13T15:49:03Z 2016-01-13T15:49:03Z 2016-01 2015-12 2016-01-11T23:00:03Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/100805 Schoutens, Kareljan, and Xiao-Gang Wen. “Simple-Current Algebra Constructions of 2+1-Dimensional Topological Orders.” Physical Review B 93, no. 4 (January 11, 2016). © 2016 American Physical Society https://orcid.org/0000-0002-5874-581X en http://dx.doi.org/10.1103/PhysRevB.93.045109 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 | Schoutens, Kareljan Wen, Xiao-Gang Simple-current algebra constructions of 2+1-dimensional topological orders |
| title | Simple-current algebra constructions of 2+1-dimensional topological orders |
| title_full | Simple-current algebra constructions of 2+1-dimensional topological orders |
| title_fullStr | Simple-current algebra constructions of 2+1-dimensional topological orders |
| title_full_unstemmed | Simple-current algebra constructions of 2+1-dimensional topological orders |
| title_short | Simple-current algebra constructions of 2+1-dimensional topological orders |
| title_sort | simple current algebra constructions of 2 1 dimensional topological orders |
| url | http://hdl.handle.net/1721.1/100805 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT schoutenskareljan simplecurrentalgebraconstructionsof21dimensionaltopologicalorders AT wenxiaogang simplecurrentalgebraconstructionsof21dimensionaltopologicalorders |