U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states
We study U(1)×U(1)⋊Z2 Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the U(1)×U(1)⋊Z2 Chern-Simons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields t...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2010
|
| Online Access: | http://hdl.handle.net/1721.1/58842 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826192467097026560 |
|---|---|
| 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 | We study U(1)×U(1)⋊Z2 Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the U(1)×U(1)⋊Z2 Chern-Simons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields the quantum dimensions of topologically distinct excitations. We find that Z2 vortices in the U(1)×U(1)⋊Z2 Chern-Simons theory carry non-Abelian statistics and we show how to compute the dimension of the Hilbert space in the presence of n pairs of Z2 vortices on a sphere. These results allow us to show that l=3 U(1)×U(1)⋊Z2 Chern-Simons theory is the low-energy effective theory for the Z4 parafermion (Read-Rezayi) fractional quantum Hall states, which occur at filling fraction ν=2/2k−3. The U(1)×U(1)⋊Z2 theory is more useful than an alternative SU(2)4×U(1)∕U(1) Chern-Simons theory because the fields are more closely related to physical degrees of freedom of the electron fluid and to an Abelian bilayer phase on the other side of a two-component to single-component quantum phase transition. We discuss the possibility of using this theory to understand further phase transitions in FQH systems, especially the ν=2∕3 phase diagram. |
| first_indexed | 2024-09-23T09:14:49Z |
| format | Article |
| id | mit-1721.1/58842 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:14:49Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/588422022-09-30T14:06:32Z U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states Barkeshli, Maissam Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Barkeshli, Maissam Wen, Xiao-Gang We study U(1)×U(1)⋊Z2 Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the U(1)×U(1)⋊Z2 Chern-Simons theory, we show how to compute the dimension of its Hilbert space on genus g surfaces and how this yields the quantum dimensions of topologically distinct excitations. We find that Z2 vortices in the U(1)×U(1)⋊Z2 Chern-Simons theory carry non-Abelian statistics and we show how to compute the dimension of the Hilbert space in the presence of n pairs of Z2 vortices on a sphere. These results allow us to show that l=3 U(1)×U(1)⋊Z2 Chern-Simons theory is the low-energy effective theory for the Z4 parafermion (Read-Rezayi) fractional quantum Hall states, which occur at filling fraction ν=2/2k−3. The U(1)×U(1)⋊Z2 theory is more useful than an alternative SU(2)4×U(1)∕U(1) Chern-Simons theory because the fields are more closely related to physical degrees of freedom of the electron fluid and to an Abelian bilayer phase on the other side of a two-component to single-component quantum phase transition. We discuss the possibility of using this theory to understand further phase transitions in FQH systems, especially the ν=2∕3 phase diagram. 2010-10-04T13:02:47Z 2010-10-04T13:02:47Z 2010-01 2009-10 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/58842 Maissam Barkeshli and Xiao-Gang Wen (2010). U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states. Phys. rev. B 81: 045323/1-18. © 2010 The American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.81.045323 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 U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states |
| title | U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states |
| title_full | U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states |
| title_fullStr | U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states |
| title_full_unstemmed | U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states |
| title_short | U(1) X U(1) XI Z(2) Chern-Simons theory and Z(4) parafermion fractional quantum Hall states |
| title_sort | u 1 x u 1 xi z 2 chern simons theory and z 4 parafermion fractional quantum hall states |
| url | http://hdl.handle.net/1721.1/58842 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT barkeshlimaissam u1xu1xiz2chernsimonstheoryandz4parafermionfractionalquantumhallstates AT wenxiaogang u1xu1xiz2chernsimonstheoryandz4parafermionfractionalquantumhallstates |