Structure of quasiparticles and their fusion algebra in fractional quantum Hall states
It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar qua...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2010
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| Online Access: | http://hdl.handle.net/1721.1/51878 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826203805875699712 |
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| author | Barkeshli, Maissam Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Barkeshli, Maissam Wen, Xiao-Gang |
| author_sort | Barkeshli, Maissam |
| collection | MIT |
| description | It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach. |
| first_indexed | 2024-09-23T12:43:25Z |
| format | Article |
| id | mit-1721.1/51878 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:43:25Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/518782022-09-28T09:39:47Z Structure of quasiparticles and their fusion algebra in fractional quantum Hall states Barkeshli, Maissam Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Barkeshli, Maissam Wen, Xiao-Gang It was recently discovered that fractional quantum Hall (FQH) states can be characterized quantitatively by the pattern of zeros that describe how the ground-state wave function goes to zero when electrons are brought close together. Quasiparticles in the FQH states can be described in a similar quantitative way by the pattern of zeros that result when electrons are brought close to the quasiparticles. In this paper, we combine the pattern of zeros approach and the conformal field theory (CFT) approach to calculate the topological properties of quasiparticles. We discuss how the quasiparticles in FQH states naturally form representations of a magnetic translation algebra, with members of a representation differing from each other by Abelian quasiparticles. We find that this structure dramatically simplifies topological properties of the quasiparticles, such as their fusion rules, charges, and scaling dimensions, and has consequences for the ground state degeneracy of FQH states on higher genus surfaces. We find constraints on the pattern of zeros of quasiparticles that can fuse together, which allow us to derive the fusion rules of quasiparticles from their pattern of zeros, at least in the case of the (generalized and composite) parafermion states. We also calculate from CFT the number of quasiparticle types in the generalized and composite parafermion states, which confirm the result obtained previously through a completely different approach. National Science Foundation 2010-03-02T15:17:17Z 2010-03-02T15:17:17Z 2009-05 2008-09 Article http://purl.org/eprint/type/JournalArticle 1550-235X 1098-0121 http://hdl.handle.net/1721.1/51878 Barkeshli, Maissam , and Xiao-Gang Wen. “Structure of quasiparticles and their fusion algebra in fractional quantum Hall states.” Physical Review B 79.19 (2009): 195132. © 2009 The American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.79.195132 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. application/pdf American Physical Society APS |
| spellingShingle | Barkeshli, Maissam Wen, Xiao-Gang Structure of quasiparticles and their fusion algebra in fractional quantum Hall states |
| title | Structure of quasiparticles and their fusion algebra in fractional quantum Hall states |
| title_full | Structure of quasiparticles and their fusion algebra in fractional quantum Hall states |
| title_fullStr | Structure of quasiparticles and their fusion algebra in fractional quantum Hall states |
| title_full_unstemmed | Structure of quasiparticles and their fusion algebra in fractional quantum Hall states |
| title_short | Structure of quasiparticles and their fusion algebra in fractional quantum Hall states |
| title_sort | structure of quasiparticles and their fusion algebra in fractional quantum hall states |
| url | http://hdl.handle.net/1721.1/51878 https://orcid.org/0000-0002-5874-581X |
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