Classification of gapped symmetric phases in one-dimensional spin systems
Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting qua...
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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/1721.1/63135 https://orcid.org/0000-0002-5874-581X |
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| author | Chen, Xie Gu, Zheng-Cheng Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Chen, Xie Gu, Zheng-Cheng Wen, Xiao-Gang |
| author_sort | Chen, Xie |
| collection | MIT |
| description | Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are short-range correlated. Based on the local unitary equivalence relation between short-range-correlated states in the same phase, we classify possible quantum phases for one-dimensional (1D) matrix product states, which represent well the class of 1D gapped ground states. We find that in the absence of any symmetry all states are equivalent to trivial product states, which means that there is no topological order in 1D. However, if a certain symmetry is required, many phases exist with different symmetry-protected topological orders. The symmetric local unitary equivalence relation also allows us to obtain some simple results for quantum phases in higher dimensions when some symmetries are present. |
| first_indexed | 2024-09-23T13:23:21Z |
| format | Article |
| id | mit-1721.1/63135 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:23:21Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/631352022-09-28T13:47:47Z Classification of gapped symmetric phases in one-dimensional spin systems Chen, Xie Gu, Zheng-Cheng Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang Chen, Xie Wen, Xiao-Gang Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are short-range correlated. Based on the local unitary equivalence relation between short-range-correlated states in the same phase, we classify possible quantum phases for one-dimensional (1D) matrix product states, which represent well the class of 1D gapped ground states. We find that in the absence of any symmetry all states are equivalent to trivial product states, which means that there is no topological order in 1D. However, if a certain symmetry is required, many phases exist with different symmetry-protected topological orders. The symmetric local unitary equivalence relation also allows us to obtain some simple results for quantum phases in higher dimensions when some symmetries are present. 2011-05-27T19:28:07Z 2011-05-27T19:28:07Z 2011-01 2010-11 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/63135 Chen, Xie, Zheng-Cheng Gu, and Xiao-Gang Wen. “Classification of Gapped Symmetric Phases in One-dimensional Spin Systems.” Physical Review B 83.3 (2011) : 035107. © 2011 American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.83.035107 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 | Chen, Xie Gu, Zheng-Cheng Wen, Xiao-Gang Classification of gapped symmetric phases in one-dimensional spin systems |
| title | Classification of gapped symmetric phases in one-dimensional spin systems |
| title_full | Classification of gapped symmetric phases in one-dimensional spin systems |
| title_fullStr | Classification of gapped symmetric phases in one-dimensional spin systems |
| title_full_unstemmed | Classification of gapped symmetric phases in one-dimensional spin systems |
| title_short | Classification of gapped symmetric phases in one-dimensional spin systems |
| title_sort | classification of gapped symmetric phases in one dimensional spin systems |
| url | http://hdl.handle.net/1721.1/63135 https://orcid.org/0000-0002-5874-581X |
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