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dc.contributor.authorGu, Zheng-Cheng
dc.contributor.authorWang, Zhenghan
dc.contributor.authorWen, Xiao-Gang
dc.date.accessioned2015-04-03T16:30:43Z
dc.date.available2015-04-03T16:30:43Z
dc.date.issued2015-03
dc.date.submitted2015-01
dc.identifier.issn1098-0121
dc.identifier.issn1550-235X
dc.identifier.urihttp://hdl.handle.net/1721.1/96372
dc.description.abstractThe string-net approach by Levin and Wen, and the local unitary transformation approach by Chen, Gu, and Wen, provide ways to classify topological orders with gappable edge in two-dimensional (2D) bosonic systems. The two approaches reveal that the mathematical framework for (2+1)-dimensional (2+1)D bosonic topological order with gappable edge is closely related to unitary fusion category theory. In this paper, we generalize these systematic descriptions of topological orders to 2D fermion systems. We find a classification of (2+1)D fermionic topological orders with gappable edge in terms of the following set of data (N[ij over k], F[ij over k], F[ijm,αβ over jkn,χδ], d[subscript i]), which satisfy a set of nonlinear algebraic equations. The exactly soluble Hamiltonians can be constructed from the above data on any lattices to realize the corresponding topological orders. When F[ij over k] = 0, our result recovers the previous classification of 2 + 1D bosonic topological orders with gappable edge.en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMR-1005541)en_US
dc.description.sponsorshipNational Natural Science Foundation (China) (Grant 11274192)en_US
dc.description.sponsorshipBMO Financial Groupen_US
dc.description.sponsorshipTempleton Foundation (Grant 39901)en_US
dc.description.sponsorshipCanada. Industry Canadaen_US
dc.description.sponsorshipOntario. Ministry of Research and Innovationen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevB.91.125149en_US
dc.rightsArticle 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.sourceAmerican Physical Societyen_US
dc.titleClassification of two-dimensional fermionic and bosonic topological ordersen_US
dc.typeArticleen_US
dc.identifier.citationGu, Zheng-Cheng, Zhenghan Wang, and Xiao-Gang Wen. "Classification of two-dimensional fermionic and bosonic topological orders." Phys. Rev. B 91, 125149 (March 2015). © 2015 American Physical Societyen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.contributor.mitauthorWen, Xiao-Gangen_US
dc.relation.journalPhysical Review Ben_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2015-03-31T22:00:06Z
dc.language.rfc3066en
dc.rights.holderAmerican Physical Society
dspace.orderedauthorsGu, Zheng-Cheng; Wang, Zhenghan; Wen, Xiao-Gangen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-5874-581X
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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