Gapped quantum phases for the S=1 spin chain with D2h symmetry
We study different quantum phases in integer spin systems with on-site D[subscript 2h]=D[subscript 2]⊗Z[subscript 2] and translation symmetry. We find four distinct nontrivial phases in S=1 spin chains despite the fact that they all have the same symmetry. All four phases have gapped bulk excitation...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/67349 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826211126090661888 |
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| author | Liu, Zheng-Xin Liu, Min Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Liu, Zheng-Xin Liu, Min Wen, Xiao-Gang |
| author_sort | Liu, Zheng-Xin |
| collection | MIT |
| description | We study different quantum phases in integer spin systems with on-site D[subscript 2h]=D[subscript 2]⊗Z[subscript 2] and translation symmetry. We find four distinct nontrivial phases in S=1 spin chains despite the fact that they all have the same symmetry. All four phases have gapped bulk excitations, doubly degenerate end states, and the doubly degenerate entanglement spectrum. These nontrivial phases are examples of symmetry-protected topological (SPT) phases introduced by Gu and Wen [ Phys. Rev. B 80 155131 (2009)]. One of the SPT phases corresponds to the Haldane phase and the other three are new. These four SPT phases can be distinguished experimentally by their different responses of the end states to weak external magnetic fields. According to the Chen–Gu–Wen classification, the D[subscript 2h] symmetric spin chain can have a total of 64 SPT phases that do not break the symmetry. Here we constructed seven nontrivial phases from the seven classes of nontrivial projective representations of the D[subscript 2h] group. Four of these are found in S=1 spin chains and studied in this paper. |
| first_indexed | 2024-09-23T15:01:18Z |
| format | Article |
| id | mit-1721.1/67349 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:01:18Z |
| publishDate | 2011 |
| publisher | American Physical Society |
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| spelling | mit-1721.1/673492022-10-01T23:59:57Z Gapped quantum phases for the S=1 spin chain with D2h symmetry Liu, Zheng-Xin Liu, Min Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Wen, Xiao-Gang We study different quantum phases in integer spin systems with on-site D[subscript 2h]=D[subscript 2]⊗Z[subscript 2] and translation symmetry. We find four distinct nontrivial phases in S=1 spin chains despite the fact that they all have the same symmetry. All four phases have gapped bulk excitations, doubly degenerate end states, and the doubly degenerate entanglement spectrum. These nontrivial phases are examples of symmetry-protected topological (SPT) phases introduced by Gu and Wen [ Phys. Rev. B 80 155131 (2009)]. One of the SPT phases corresponds to the Haldane phase and the other three are new. These four SPT phases can be distinguished experimentally by their different responses of the end states to weak external magnetic fields. According to the Chen–Gu–Wen classification, the D[subscript 2h] symmetric spin chain can have a total of 64 SPT phases that do not break the symmetry. Here we constructed seven nontrivial phases from the seven classes of nontrivial projective representations of the D[subscript 2h] group. Four of these are found in S=1 spin chains and studied in this paper. National Science Foundation (U.S.) (Grant DMR-1005541) National Natural Science Foundation (China) (11074140) 2011-12-02T17:31:29Z 2011-12-02T17:31:29Z 2011-08 2011-06 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/67349 Liu, Zheng-Xin, Min Liu, and Xiao-Gang Wen. “Gapped quantum phases for the S=1 spin chain with D_{2h} symmetry.” Physical Review B 84 (2011): n. pag. Web. 2 Dec. 2011. © 2011 American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.84.075135 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 | Liu, Zheng-Xin Liu, Min Wen, Xiao-Gang Gapped quantum phases for the S=1 spin chain with D2h symmetry |
| title | Gapped quantum phases for the S=1 spin chain with D2h symmetry |
| title_full | Gapped quantum phases for the S=1 spin chain with D2h symmetry |
| title_fullStr | Gapped quantum phases for the S=1 spin chain with D2h symmetry |
| title_full_unstemmed | Gapped quantum phases for the S=1 spin chain with D2h symmetry |
| title_short | Gapped quantum phases for the S=1 spin chain with D2h symmetry |
| title_sort | gapped quantum phases for the s 1 spin chain with d2h symmetry |
| url | http://hdl.handle.net/1721.1/67349 https://orcid.org/0000-0002-5874-581X |
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