Chiral symmetry on the edge of two-dimensional symmetry protected topological phases
Symmetry protected topological (SPT) states are short-range entangled states with symmetry. The boundary of a SPT phases has either gapless excitations or degenerate ground states, around a gapped bulk. Recently, we proposed a systematic construction of SPT phases in interacting bosonic systems, how...
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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/1721.1/88750 https://orcid.org/0000-0002-5874-581X |
| _version_ | 1811095402470965248 |
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| author | Chen, Xie Wen, Xiao-Gang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Chen, Xie Wen, Xiao-Gang |
| author_sort | Chen, Xie |
| collection | MIT |
| description | Symmetry protected topological (SPT) states are short-range entangled states with symmetry. The boundary of a SPT phases has either gapless excitations or degenerate ground states, around a gapped bulk. Recently, we proposed a systematic construction of SPT phases in interacting bosonic systems, however it is not very clear what is the form of the low-energy excitations on the gapless edge. In this paper, we answer this question for two-dimensional (2D) bosonic SPT phases with Z[subscript N] and U(1) symmetry. We find that while the low-energy modes of the gapless edges are nonchiral, symmetry acts on them in a “chiral” way, i.e., acts on the right movers and the left movers differently. This special realization of symmetry protects the gaplessness of the otherwise unstable edge states by prohibiting a direct scattering between the left and right movers. Moreover, understanding of the low-energy effective theory leads to experimental predictions about the SPT phases. In particular, we find that all the 2D U(1) SPT phases have even integer quantized Hall conductance. |
| first_indexed | 2024-09-23T16:15:53Z |
| format | Article |
| id | mit-1721.1/88750 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:15:53Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/887502022-09-29T19:14:22Z Chiral symmetry on the edge of two-dimensional symmetry protected topological phases Chen, Xie Wen, Xiao-Gang Massachusetts Institute of Technology. Department of Physics Chen, Xie Wen, Xiao-Gang Symmetry protected topological (SPT) states are short-range entangled states with symmetry. The boundary of a SPT phases has either gapless excitations or degenerate ground states, around a gapped bulk. Recently, we proposed a systematic construction of SPT phases in interacting bosonic systems, however it is not very clear what is the form of the low-energy excitations on the gapless edge. In this paper, we answer this question for two-dimensional (2D) bosonic SPT phases with Z[subscript N] and U(1) symmetry. We find that while the low-energy modes of the gapless edges are nonchiral, symmetry acts on them in a “chiral” way, i.e., acts on the right movers and the left movers differently. This special realization of symmetry protects the gaplessness of the otherwise unstable edge states by prohibiting a direct scattering between the left and right movers. Moreover, understanding of the low-energy effective theory leads to experimental predictions about the SPT phases. In particular, we find that all the 2D U(1) SPT phases have even integer quantized Hall conductance. National Science Foundation (U.S.) (Grant DMR-1005541) 2014-08-18T14:59:48Z 2014-08-18T14:59:48Z 2012-12 2012-07 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/88750 Chen, Xie, and Xiao-Gang Wen. “Chiral Symmetry on the Edge of Two-Dimensional Symmetry Protected Topological Phases.” Phys. Rev. B 86, no. 23 (December 2012). © 2012 American Physical Society https://orcid.org/0000-0002-5874-581X en_US http://dx.doi.org/10.1103/PhysRevB.86.235135 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 American Physical Society |
| spellingShingle | Chen, Xie Wen, Xiao-Gang Chiral symmetry on the edge of two-dimensional symmetry protected topological phases |
| title | Chiral symmetry on the edge of two-dimensional symmetry protected topological phases |
| title_full | Chiral symmetry on the edge of two-dimensional symmetry protected topological phases |
| title_fullStr | Chiral symmetry on the edge of two-dimensional symmetry protected topological phases |
| title_full_unstemmed | Chiral symmetry on the edge of two-dimensional symmetry protected topological phases |
| title_short | Chiral symmetry on the edge of two-dimensional symmetry protected topological phases |
| title_sort | chiral symmetry on the edge of two dimensional symmetry protected topological phases |
| url | http://hdl.handle.net/1721.1/88750 https://orcid.org/0000-0002-5874-581X |
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