Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry
In Liu et al. [ Phys. Rev. B 84 075135 (2011)] we studied eight gapped symmetric quantum phases in S=1 spin chains/ladders which respect a discrete spin rotation D[subscript 2]⊂SO(3) and time reversal T symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symm...
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| Format: | Article |
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American Physical Society (APS)
2012
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| Online Access: | http://hdl.handle.net/1721.1/69567 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826188424886878208 |
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| author | Liu, Zheng-Xin Chen, Xie Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Liu, Zheng-Xin Chen, Xie Wen, Xiao-Gang |
| author_sort | Liu, Zheng-Xin |
| collection | MIT |
| description | In Liu et al. [ Phys. Rev. B 84 075135 (2011)] we studied eight gapped symmetric quantum phases in S=1 spin chains/ladders which respect a discrete spin rotation D[subscript 2]⊂SO(3) and time reversal T symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of one-dimensional (1D) integer spin systems with D[subscript 2]+T symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in S=1 spin chain or spin ladder models. The gapped symmetric phases protected by subgroups of D[subscript 2]+T are also studied. Again, all these phases can be distinguished by physically measuring their end “spins.” |
| first_indexed | 2024-09-23T07:59:26Z |
| format | Article |
| id | mit-1721.1/69567 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:59:26Z |
| publishDate | 2012 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/695672022-09-23T10:06:56Z Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry Symmetry-protected topological orders of one-dimensional spin systems with D2+T symmetry Liu, Zheng-Xin Chen, Xie Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Liu, Zheng-Xin Chen, Xie Wen, Xiao-Gang In Liu et al. [ Phys. Rev. B 84 075135 (2011)] we studied eight gapped symmetric quantum phases in S=1 spin chains/ladders which respect a discrete spin rotation D[subscript 2]⊂SO(3) and time reversal T symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of one-dimensional (1D) integer spin systems with D[subscript 2]+T symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in S=1 spin chain or spin ladder models. The gapped symmetric phases protected by subgroups of D[subscript 2]+T are also studied. Again, all these phases can be distinguished by physically measuring their end “spins.” National Science Foundation (U.S.) (Grant No. DMR-1005541) National Natural Science Foundation (China) (NSFC 11074140) 2012-03-02T18:19:18Z 2012-03-02T18:19:18Z 2011-11 2011-10 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/69567 Liu, Zheng-Xin, Xie Chen, and Xiao-Gang Wen. “Symmetry-protected Topological Orders of One-dimensional Spin Systems with D_{2}+T Symmetry.” Physical Review B 84.19 (2011): n. pag. Web. 2 Mar. 2012. © 2011 American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.84.195145 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) APS |
| spellingShingle | Liu, Zheng-Xin Chen, Xie Wen, Xiao-Gang Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry |
| title | Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry |
| title_full | Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry |
| title_fullStr | Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry |
| title_full_unstemmed | Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry |
| title_short | Symmetry-protected topological orders of one-dimensional spin systems with D[subscript 2]+T symmetry |
| title_sort | symmetry protected topological orders of one dimensional spin systems with d subscript 2 t symmetry |
| url | http://hdl.handle.net/1721.1/69567 https://orcid.org/0000-0002-5874-581X |
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