Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states
The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the simpler integer quantum Hall states. Here we show how to apply the projective cons...
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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/1721.1/58690 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826192988440625152 |
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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 | The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the simpler integer quantum Hall states. Here we show how to apply the projective construction to the Z[subscript k] parafermion (Laughlin/Moore-Read/Read-Rezayi) FQH states, which occur at filling fraction ν=k/(kM+2). This allows us to derive the bulk low-energy effective field theory for these topological phases, which is found to be a Chern-Simons theory at level 1 with a U(M)×Sp(2k) gauge field. This approach also helps us understand the non-Abelian quasiholes in terms of holes of the integer quantum Hall states. |
| first_indexed | 2024-09-23T09:32:14Z |
| format | Article |
| id | mit-1721.1/58690 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:32:14Z |
| publishDate | 2010 |
| publisher | American Physical Society |
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| spelling | mit-1721.1/586902022-09-30T15:05:37Z Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states Effective field theory and projective construction for Zk parafermion fractional quantum Hall states Barkeshli, Maissam Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Wen, Xiao-Gang Barkeshli, Maissam The projective construction is a powerful approach to deriving the bulk and edge field theories of non-Abelian fractional quantum Hall (FQH) states and yields an understanding of non-Abelian FQH states in terms of the simpler integer quantum Hall states. Here we show how to apply the projective construction to the Z[subscript k] parafermion (Laughlin/Moore-Read/Read-Rezayi) FQH states, which occur at filling fraction ν=k/(kM+2). This allows us to derive the bulk low-energy effective field theory for these topological phases, which is found to be a Chern-Simons theory at level 1 with a U(M)×Sp(2k) gauge field. This approach also helps us understand the non-Abelian quasiholes in terms of holes of the integer quantum Hall states. National Science Foundation (U.S.) (Grant No. DMR- 0706078) 2010-09-23T20:31:05Z 2010-09-23T20:31:05Z 2010-04 2009-11 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/58690 Barkeshli, Maissam, and Xiao-Gang Wen. “Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states.” Physical Review B 81.15 (2010): 155302. © 2010 The American Physical Society. https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.81.155302 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 Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states |
| title | Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states |
| title_full | Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states |
| title_fullStr | Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states |
| title_full_unstemmed | Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states |
| title_short | Effective field theory and projective construction for Z[subscript k] parafermion fractional quantum Hall states |
| title_sort | effective field theory and projective construction for z subscript k parafermion fractional quantum hall states |
| url | http://hdl.handle.net/1721.1/58690 https://orcid.org/0000-0002-5874-581X |
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