Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model
Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript N] Abelian gauge theory. We find that lattice dislocation defects in the model...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2013
|
| Online Access: | http://hdl.handle.net/1721.1/75856 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826216990368333824 |
|---|---|
| author | You, Yi-Zhuang Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics You, Yi-Zhuang Wen, Xiao-Gang |
| author_sort | You, Yi-Zhuang |
| collection | MIT |
| description | Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript N] Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension √N. Exchanging dislocations can produce topologically protected projective non-Abelian geometric phases. Therefore, we discover a kind of (projective) non-Abelian anyon that appears as the dislocations in an Abelian Z[subscript N] rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes. |
| first_indexed | 2024-09-23T16:56:19Z |
| format | Article |
| id | mit-1721.1/75856 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:56:19Z |
| publishDate | 2013 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/758562022-10-03T09:15:17Z Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model You, Yi-Zhuang Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript N] Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension √N. Exchanging dislocations can produce topologically protected projective non-Abelian geometric phases. Therefore, we discover a kind of (projective) non-Abelian anyon that appears as the dislocations in an Abelian Z[subscript N] rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes. National Science Foundation (U.S.) (Grant DMR-1005541) National Natural Science Foundation (China) (11074140) 2013-01-07T19:47:30Z 2013-01-07T19:47:30Z 2012-10 2012-04 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/75856 You, Yi-Zhuang, and Xiao-Gang Wen. “Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model.” Physical Review B 86.16 (2012). © 2012 American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.86.161107 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 | You, Yi-Zhuang Wen, Xiao-Gang Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model |
| title | Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model |
| title_full | Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model |
| title_fullStr | Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model |
| title_full_unstemmed | Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model |
| title_short | Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model |
| title_sort | projective non abelian statistics of dislocation defects in a z subscript n rotor model |
| url | http://hdl.handle.net/1721.1/75856 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT youyizhuang projectivenonabelianstatisticsofdislocationdefectsinazsubscriptnrotormodel AT wenxiaogang projectivenonabelianstatisticsofdislocationdefectsinazsubscriptnrotormodel |