dc.contributor.author | Chen, Xie | |
dc.contributor.author | Liu, Zheng-Xin | |
dc.contributor.author | Wen, Xiao-Gang | |
dc.date.accessioned | 2012-08-08T15:24:56Z | |
dc.date.available | 2012-08-08T15:24:56Z | |
dc.date.issued | 2011-12 | |
dc.date.submitted | 2011-10 | |
dc.identifier.issn | 1098-0121 | |
dc.identifier.issn | 1550-235X | |
dc.identifier.uri | http://hdl.handle.net/1721.1/72029 | |
dc.description.abstract | Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite Z[subscript 2] symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related to a nontrivial 3-cocycle of the Z[subscript 2] group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry-protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if Z[subscript 2] symmetry is not broken. We prove the latter by developing the tool of a matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and reveal the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with onsite Z[subscript 2] symmetry-protected topological order. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (grant no. NSFC 11074140) | en_US |
dc.language.iso | en_US | |
dc.publisher | American Physical Society | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1103/PhysRevB.84.235141 | en_US |
dc.rights | 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. | en_US |
dc.source | APS | en_US |
dc.title | Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Chen, Xie, Zheng-Xin Liu, and Xiao-Gang Wen. “Two-dimensional Symmetry-protected Topological Orders and Their Protected Gapless Edge Excitations.” Physical Review B 84.23 (2011): 235141-1-235141-13. ©2011 American Physical Society | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Physics | en_US |
dc.contributor.approver | Wen, Xiao-Gang | |
dc.contributor.mitauthor | Chen, Xie | |
dc.contributor.mitauthor | Liu, Zheng-Xin | |
dc.contributor.mitauthor | Wen, Xiao-Gang | |
dc.relation.journal | Physical Review B | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Chen, Xie; Liu, Zheng-Xin; Wen, Xiao-Gang | en |
dc.identifier.orcid | https://orcid.org/0000-0002-5874-581X | |
mit.license | PUBLISHER_POLICY | en_US |
mit.metadata.status | Complete | |