The Quantum Double Model with Boundary: Condensations and Symmetries
Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2012
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| Online Access: | http://hdl.handle.net/1721.1/71667 https://orcid.org/0000-0003-4626-5648 |
| _version_ | 1811088578800779264 |
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| author | Beigi, Salman Shor, Peter W. Whalen, Daniel |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Beigi, Salman Shor, Peter W. Whalen, Daniel |
| author_sort | Beigi, Salman |
| collection | MIT |
| description | Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to the boundary. We then consider two phases of the quantum double model corresponding to two groups with a domain wall between them, and study the tunneling of anyons from one phase to the other. Using this framework we discuss the necessary and sufficient conditions when two different groups give the same anyon types. As an application we show that in the quantum double model for S 3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. This group is indeed a special case of groups of the form of the semidirect product of the additive and multiplicative groups of a finite field, for all of which we prove a similar symmetry. |
| first_indexed | 2024-09-23T14:04:15Z |
| format | Article |
| id | mit-1721.1/71667 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:04:15Z |
| publishDate | 2012 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/716672022-09-28T18:07:58Z The Quantum Double Model with Boundary: Condensations and Symmetries Beigi, Salman Shor, Peter W. Whalen, Daniel Massachusetts Institute of Technology. Department of Mathematics Shor, Peter W. Shor, Peter W. Whalen, Daniel Associated to every finite group, Kitaev has defined the quantum double model for every orientable surface without boundary. In this paper, we define boundaries for this model and characterize condensations; that is, we find all quasi-particle excitations (anyons) which disappear when they move to the boundary. We then consider two phases of the quantum double model corresponding to two groups with a domain wall between them, and study the tunneling of anyons from one phase to the other. Using this framework we discuss the necessary and sufficient conditions when two different groups give the same anyon types. As an application we show that in the quantum double model for S 3 (the permutation group over three letters) there is a chargeon and a fluxion which are not distinguishable. This group is indeed a special case of groups of the form of the semidirect product of the additive and multiplicative groups of a finite field, for all of which we prove a similar symmetry. 2012-07-17T19:43:23Z 2012-07-17T19:43:23Z 2011-06 2010-08 Article http://purl.org/eprint/type/JournalArticle 0010-3616 1432-0916 http://hdl.handle.net/1721.1/71667 Beigi, Salman, Peter W. Shor, and Daniel Whalen. “The Quantum Double Model with Boundary: Condensations and Symmetries.” Communications in Mathematical Physics 306.3 (2011): 663–694. Web. https://orcid.org/0000-0003-4626-5648 en_US http://dx.doi.org/10.1007/s00220-011-1294-x Communications in Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Beigi, Salman Shor, Peter W. Whalen, Daniel The Quantum Double Model with Boundary: Condensations and Symmetries |
| title | The Quantum Double Model with Boundary: Condensations and Symmetries |
| title_full | The Quantum Double Model with Boundary: Condensations and Symmetries |
| title_fullStr | The Quantum Double Model with Boundary: Condensations and Symmetries |
| title_full_unstemmed | The Quantum Double Model with Boundary: Condensations and Symmetries |
| title_short | The Quantum Double Model with Boundary: Condensations and Symmetries |
| title_sort | quantum double model with boundary condensations and symmetries |
| url | http://hdl.handle.net/1721.1/71667 https://orcid.org/0000-0003-4626-5648 |
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