Boundary-bulk relation in topological orders
In this paper, we study the relation between an anomaly-free n+1 D topological order, which are often called n+1 D topological order in physics literature, and its n D gapped boundary phases. We argue that the n+1 D bulk anomaly-free topological order for a given n D gapped boundary phase is unique....
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| Format: | Article |
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Elsevier
2017
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| Online Access: | http://hdl.handle.net/1721.1/111839 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826214100424720384 |
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| author | Kong, Liang Zheng, Hao Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Kong, Liang Zheng, Hao Wen, Xiao-Gang |
| author_sort | Kong, Liang |
| collection | MIT |
| description | In this paper, we study the relation between an anomaly-free n+1 D topological order, which are often called n+1 D topological order in physics literature, and its n D gapped boundary phases. We argue that the n+1 D bulk anomaly-free topological order for a given n D gapped boundary phase is unique. This uniqueness defines the notion of the “ bulk ” for a given gapped boundary phase. In this paper, we show that the n+1 D “ bulk ” phase is given by the “center” of the n D boundary phase. In other words, the geometric notion of the “ bulk ” corresponds precisely to the algebraic notion of the “center”. We achieve this by first introducing the notion of a morphism between two (potentially anomalous) topological orders of the same dimension, then proving that the notion of the “ bulk ” satisfies the same universal property as that of the “center” of an algebra in mathematics, i.e. “ bulk = center”. The entire argument does not require us to know the precise mathematical description of a (potentially anomalous) topological order. This result leads to concrete physical predictions. |
| first_indexed | 2024-09-23T15:59:48Z |
| format | Article |
| id | mit-1721.1/111839 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:59:48Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1118392022-09-29T17:33:50Z Boundary-bulk relation in topological orders Kong, Liang Zheng, Hao Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang In this paper, we study the relation between an anomaly-free n+1 D topological order, which are often called n+1 D topological order in physics literature, and its n D gapped boundary phases. We argue that the n+1 D bulk anomaly-free topological order for a given n D gapped boundary phase is unique. This uniqueness defines the notion of the “ bulk ” for a given gapped boundary phase. In this paper, we show that the n+1 D “ bulk ” phase is given by the “center” of the n D boundary phase. In other words, the geometric notion of the “ bulk ” corresponds precisely to the algebraic notion of the “center”. We achieve this by first introducing the notion of a morphism between two (potentially anomalous) topological orders of the same dimension, then proving that the notion of the “ bulk ” satisfies the same universal property as that of the “center” of an algebra in mathematics, i.e. “ bulk = center”. The entire argument does not require us to know the precise mathematical description of a (potentially anomalous) topological order. This result leads to concrete physical predictions. National Science Foundation (U.S.) (Grant DMR-1506475) National Science Foundation (U.S.) (Grant NSFC11274192) 2017-10-11T13:04:08Z 2017-10-11T13:04:08Z 2017-07 2017-06 2017-09-19T17:30:06Z Article http://purl.org/eprint/type/JournalArticle 0550-3213 http://hdl.handle.net/1721.1/111839 Kong, Liang, et al. “Boundary-Bulk Relation in Topological Orders.” Nuclear Physics B 922 (September 2017): 62–76 © 2017 The Author(s) https://orcid.org/0000-0002-5874-581X http://dx.doi.org/10.1016/j.nuclphysb.2017.06.023 Nuclear Physics B Creative Commons Attribution http://creativecommons.org/licenses/by/3.0/ The Author(s) application/pdf Elsevier TopicHub SCOAP3 |
| spellingShingle | Kong, Liang Zheng, Hao Wen, Xiao-Gang Boundary-bulk relation in topological orders |
| title | Boundary-bulk relation in topological orders |
| title_full | Boundary-bulk relation in topological orders |
| title_fullStr | Boundary-bulk relation in topological orders |
| title_full_unstemmed | Boundary-bulk relation in topological orders |
| title_short | Boundary-bulk relation in topological orders |
| title_sort | boundary bulk relation in topological orders |
| url | http://hdl.handle.net/1721.1/111839 https://orcid.org/0000-0002-5874-581X |
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