Classification of symmetry-protected phases for interacting fermions in two dimensions
Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H[superscript 3](G,U(1)). Later, group supercohomology was proposed as a partial classification for SPT phas...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/115315 |
| _version_ | 1811079399713275904 |
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| author | Cheng, Meng Bi, Zhen You, Yi-Zhuang Gu, Zheng-Cheng |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Cheng, Meng Bi, Zhen You, Yi-Zhuang Gu, Zheng-Cheng |
| author_sort | Cheng, Meng |
| collection | MIT |
| description | Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H[superscript 3](G,U(1)). Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H[superscript 1](G,Z[subscript 2]) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G×Z[subscript 2][superscript f] is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry. |
| first_indexed | 2024-09-23T11:14:24Z |
| format | Article |
| id | mit-1721.1/115315 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:14:24Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1153152022-10-01T02:16:56Z Classification of symmetry-protected phases for interacting fermions in two dimensions Cheng, Meng Bi, Zhen You, Yi-Zhuang Gu, Zheng-Cheng Massachusetts Institute of Technology. Department of Physics Bi, Zhen Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H[superscript 3](G,U(1)). Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H[superscript 1](G,Z[subscript 2]) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G×Z[subscript 2][superscript f] is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry. 2018-05-11T14:50:37Z 2018-05-11T14:50:37Z 2018-05 2018-04 2018-05-09T18:00:16Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/115315 Cheng, Meng et al. "Classification of symmetry-protected phases for interacting fermions in two dimensions." Physical Review B 97, 20 (May 2018): 205109 © 2018 American Physical Society en http://dx.doi.org/10.1103/PhysRevB.97.205109 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Cheng, Meng Bi, Zhen You, Yi-Zhuang Gu, Zheng-Cheng Classification of symmetry-protected phases for interacting fermions in two dimensions |
| title | Classification of symmetry-protected phases for interacting fermions in two dimensions |
| title_full | Classification of symmetry-protected phases for interacting fermions in two dimensions |
| title_fullStr | Classification of symmetry-protected phases for interacting fermions in two dimensions |
| title_full_unstemmed | Classification of symmetry-protected phases for interacting fermions in two dimensions |
| title_short | Classification of symmetry-protected phases for interacting fermions in two dimensions |
| title_sort | classification of symmetry protected phases for interacting fermions in two dimensions |
| url | http://hdl.handle.net/1721.1/115315 |
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