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dc.contributor.authorWen, Xiao-Gang
dc.date.accessioned2014-08-21T15:00:30Z
dc.date.available2014-08-21T15:00:30Z
dc.date.issued2014-01
dc.date.submitted2013-11
dc.identifier.issn1098-0121
dc.identifier.issn1550-235X
dc.identifier.urihttp://hdl.handle.net/1721.1/88947
dc.description.abstractRecently, it was realized that quantum states of matter can be classified as long-range entangled states (i.e., with nontrivial topological order) and short-range entangled states (i.e., with trivial topological order). We can use group cohomology class H[superscript d](SG,R/Z) to systematically describe the SRE states with a symmetry SG [referred as symmetry-protected trivial (SPT) or symmetry-protected topological (SPT) states] in d-dimensional space-time. In this paper, we study the physical properties of those SPT states, such as the fractionalization of the quantum numbers of the global symmetry on some designed point defects and the appearance of fractionalized SPT states on some designed defect lines/membranes. Those physical properties are SPT invariants of the SPT states which allow us to experimentally or numerically detect those SPT states, i.e., to measure the elements in H[superscript d](G,R/Z) that label different SPT states. For example, 2+1-dimensional bosonic SPT states with Z[subscript n] symmetry are classified by a Z[subscript n] integer m ∈ H[superscript 3](Z[subscript n],R/Z) = Z[subscript n]. We find that n identical monodromy defects, in a Z[subscript n] SPT state labeled by m, carry a total Z[subscript n] charge 2m (which is not a multiple of n in general).en_US
dc.description.sponsorshipNational Science Foundation (U.S.) (Grant DMR-1005541)en_US
dc.language.isoen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevB.89.035147en_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.titleSymmetry-protected topological invariants of symmetry-protected topological phases of interacting bosons and fermionsen_US
dc.typeArticleen_US
dc.identifier.citationWen, Xiao-Gang. “Symmetry-Protected Topological Invariants of Symmetry-Protected Topological Phases of Interacting Bosons and Fermions.” Phys. Rev. B 89, no. 3 (January 2014). © 2014 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
dspace.orderedauthorsWen, Xiao-Gangen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-5874-581X
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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