Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations
Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground-state wave functions. For systems with gapped boundaries, these quantities are representations of...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/94604 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826198762137059328 |
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| author | Moradi, Heidar Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Moradi, Heidar Wen, Xiao-Gang |
| author_sort | Moradi, Heidar |
| collection | MIT |
| description | Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground-state wave functions. For systems with gapped boundaries, these quantities are representations of the mapping class group MCG(M) of the space manifold M on which the systems live. We will here consider simple examples in three dimensions and give physical interpretation of these quantities, related to the fusion algebra and statistics of particles and string excitations. In particular, we will consider dimensional reduction from 3+1D to 2+1D, and show how the induced 2+1D topological data contain information on the fusion and the braiding of non-Abelian string excitations in 3D. These universal quantities generalize the well-known modular S and T matrices to any dimension. |
| first_indexed | 2024-09-23T11:09:40Z |
| format | Article |
| id | mit-1721.1/94604 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:09:40Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/946042022-10-01T01:41:49Z Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations Moradi, Heidar Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground-state wave functions. For systems with gapped boundaries, these quantities are representations of the mapping class group MCG(M) of the space manifold M on which the systems live. We will here consider simple examples in three dimensions and give physical interpretation of these quantities, related to the fusion algebra and statistics of particles and string excitations. In particular, we will consider dimensional reduction from 3+1D to 2+1D, and show how the induced 2+1D topological data contain information on the fusion and the braiding of non-Abelian string excitations in 3D. These universal quantities generalize the well-known modular S and T matrices to any dimension. National Science Foundation (U.S.) (Grant DMR-1005541) National Science Foundation (U.S.) (Grant NSFC 11074140) National Science Foundation (U.S.) (Grant NSFC 11274192) Templeton Foundation Canada. Industry Canada Ontario. Ministry of Research and Innovation 2015-02-18T18:28:49Z 2015-02-18T18:28:49Z 2015-02 2015-01 2015-02-17T23:00:04Z Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/94604 Moradi, Heidar, and Xiao-Gang Wen. “Universal Topological Data for Gapped Quantum Liquids in Three Dimensions and Fusion Algebra for Non-Abelian String Excitations.” Physical Review B 91.7 (2015). © 2015 American Physical Society https://orcid.org/0000-0002-5874-581X en http://dx.doi.org/10.1103/PhysRevB.91.075114 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 | Moradi, Heidar Wen, Xiao-Gang Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations |
| title | Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations |
| title_full | Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations |
| title_fullStr | Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations |
| title_full_unstemmed | Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations |
| title_short | Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations |
| title_sort | universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non abelian string excitations |
| url | http://hdl.handle.net/1721.1/94604 https://orcid.org/0000-0002-5874-581X |
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