A theory of 2+1D bosonic topological orders
© The Author(s) 2015. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. In primary school, we were told that there are four phases of matter: Solid, liquid, gas, and plasma. In college, we learned that there are much more than four pha...
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| Format: | Article |
| Language: | English |
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Oxford University Press (OUP)
2021
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| Online Access: | https://hdl.handle.net/1721.1/134484 |
| _version_ | 1811084683485642752 |
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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 | © The Author(s) 2015. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. In primary school, we were told that there are four phases of matter: Solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new 'topological' phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase-topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems). |
| first_indexed | 2024-09-23T12:55:57Z |
| format | Article |
| id | mit-1721.1/134484 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:55:57Z |
| publishDate | 2021 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1344842024-01-02T18:55:16Z A theory of 2+1D bosonic topological orders Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics © The Author(s) 2015. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. In primary school, we were told that there are four phases of matter: Solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new 'topological' phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase-topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems). 2021-10-27T20:05:13Z 2021-10-27T20:05:13Z 2016 2019-06-18T11:36:04Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/134484 en 10.1093/NSR/NWV077 National Science Review Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Wen, Xiao-Gang A theory of 2+1D bosonic topological orders |
| title | A theory of 2+1D bosonic topological orders |
| title_full | A theory of 2+1D bosonic topological orders |
| title_fullStr | A theory of 2+1D bosonic topological orders |
| title_full_unstemmed | A theory of 2+1D bosonic topological orders |
| title_short | A theory of 2+1D bosonic topological orders |
| title_sort | theory of 2 1d bosonic topological orders |
| url | https://hdl.handle.net/1721.1/134484 |
| work_keys_str_mv | AT wenxiaogang atheoryof21dbosonictopologicalorders AT wenxiaogang theoryof21dbosonictopologicalorders |