Translation-symmetry-protected topological orders in quantum spin systems
In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The lattice spin systems are translation invariant, but may break any other symmetries. We consider topologically ordered ground states tha...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/88585 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1826212745790357504 |
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| author | Kou, Su-Peng Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Kou, Su-Peng Wen, Xiao-Gang |
| author_sort | Kou, Su-Peng |
| collection | MIT |
| description | In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The lattice spin systems are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 subclasses corresponding to 16 translation-symmetry protected topological orders. We introduced four Z[subscript 2] topological indices ζ[subscript k] = 0,1 at k = (0,0), (0,π), (π,0), and (π,π) to characterize those 16 topological orders on square lattice. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on three-dimensional cubic lattice. |
| first_indexed | 2024-09-23T15:37:33Z |
| format | Article |
| id | mit-1721.1/88585 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:37:33Z |
| publishDate | 2014 |
| publisher | American Physical Society |
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| spelling | mit-1721.1/885852022-10-02T02:58:44Z Translation-symmetry-protected topological orders in quantum spin systems Kou, Su-Peng Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Wen, Xiao-Gang In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The lattice spin systems are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 subclasses corresponding to 16 translation-symmetry protected topological orders. We introduced four Z[subscript 2] topological indices ζ[subscript k] = 0,1 at k = (0,0), (0,π), (π,0), and (π,π) to characterize those 16 topological orders on square lattice. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-by-even, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on three-dimensional cubic lattice. National Science Foundation (U.S.) (Grant DMR-0706078) 2014-08-07T16:29:57Z 2014-08-07T16:29:57Z 2009-12 2009-08 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/88585 Kou, Su-Peng, and Xiao-Gang Wen. “Translation-Symmetry-Protected Topological Orders in Quantum Spin Systems.” Phys. Rev. B 80, no. 22 (December 2009). © 2009 The American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.80.224406 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 | Kou, Su-Peng Wen, Xiao-Gang Translation-symmetry-protected topological orders in quantum spin systems |
| title | Translation-symmetry-protected topological orders in quantum spin systems |
| title_full | Translation-symmetry-protected topological orders in quantum spin systems |
| title_fullStr | Translation-symmetry-protected topological orders in quantum spin systems |
| title_full_unstemmed | Translation-symmetry-protected topological orders in quantum spin systems |
| title_short | Translation-symmetry-protected topological orders in quantum spin systems |
| title_sort | translation symmetry protected topological orders in quantum spin systems |
| url | http://hdl.handle.net/1721.1/88585 https://orcid.org/0000-0002-5874-581X |
| work_keys_str_mv | AT kousupeng translationsymmetryprotectedtopologicalordersinquantumspinsystems AT wenxiaogang translationsymmetryprotectedtopologicalordersinquantumspinsystems |