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dc.contributor.authorZou, Liujun
dc.contributor.authorHaah, Jeongwan
dc.date.accessioned2017-06-22T22:36:22Z
dc.date.available2017-06-22T22:36:22Z
dc.date.issued2016-08
dc.date.submitted2016-04
dc.identifier.issn2469-9950
dc.identifier.issn2469-9969
dc.identifier.urihttp://hdl.handle.net/1721.1/110188
dc.description.abstractTopological entanglement entropy has been regarded as a smoking-gun signature of topological order in two dimensions, capturing the total quantum dimension of the topological particle content. An extrapolation method on cylinders has been used frequently to measure the topological entanglement entropy. Here, we show that a class of short-range entangled 2D states, when put on an infinite cylinder of circumference L, exhibits the entanglement Rényi entropy of any integer index α ≥ 2 that obeys S[subscript α] = aL− γ, where a,γ > 0. Under the extrapolation method, the subleading term γ would be identified as the topological entanglement entropy, which is spurious. A nonzero γ is always present if the 2D state reduces to a certain symmetry-protected topological 1D state, upon disentangling spins that are far from the entanglement cut. The internal symmetry that stabilizes γ > 0 is not necessarily a symmetry of the 2D state, but should be present after the disentangling reduction. If the symmetry is absent, γ decays exponentially in L with a characteristic length, termed as a replica correlation length, which can be arbitrarily large compared to the two-point correlation length of the 2D state. We propose a simple numerical procedure to measure the replica correlation length through replica correlation functions. We also calculate the replica correlation functions for representative wave functions of Abelian discrete gauge theories and the double semion theory in 2D, to show that they decay abruptly to zero. This supports a conjecture that the replica correlation length being small implies that the subleading term from the extrapolation method determines the total quantum dimension.en_US
dc.description.sponsorshipMassachusetts Institute of Technology (MIT Pappalardo Fellowship in Physics)en_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevB.94.075151en_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.titleSpurious long-range entanglement and replica correlation lengthen_US
dc.typeArticleen_US
dc.identifier.citationZou, Liujun, and Jeongwan Haah. “Spurious Long-Range Entanglement and Replica Correlation Length.” Physical Review B 94.7 (2016): n. pag. © 2016 American Physical Societyen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.contributor.mitauthorHaah, Jeongwan
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.updated2016-08-25T22:00:03Z
dc.language.rfc3066en
dc.rights.holderAmerican Physical Society
dspace.orderedauthorsZou, Liujun; Haah, Jeongwanen_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-4420-4932
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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