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dc.contributor.authorHaah, Jeongwan
dc.date.accessioned2017-03-03T20:11:45Z
dc.date.available2017-03-03T20:11:45Z
dc.date.issued2016-02
dc.date.submitted2014-12
dc.identifier.issn0010-3616
dc.identifier.issn1432-0916
dc.identifier.urihttp://hdl.handle.net/1721.1/107173
dc.description.abstractFor an anyon model in two spatial dimensions described by a modular tensor category, the topological S-matrix encodes the mutual braiding statistics, the quantum dimensions, and the fusion rules of anyons. It is nontrivial whether one can compute the S-matrix from a single ground state wave function. Here, we define a class of Hamiltonians consisting of local commuting projectors and an associated matrix that is invariant under local unitary transformations. We argue that the invariant is equivalent to the topological S-matrix. The definition does not require degeneracy of the ground state. We prove that the invariant depends on the state only, in the sense that it can be computed by any Hamiltonian in the class of which the state is a ground state. As a corollary, we prove that any local quantum circuit that connects two ground states of quantum double models (discrete gauge theories) with non-isomorphic abelian groups must have depth that is at least linear in the system’s diameter. As a tool for the proof, a manifestly Hamiltonian-independent notion of locally invisible operators is introduced. This gives a sufficient condition for a many-body state not to be generated from a product state by any small depth quantum circuit; this is a many-body entanglement witness.en_US
dc.description.sponsorshipMIT Department of Physics Pappalardo Programen_US
dc.publisherSpringer Berlin Heidelbergen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00220-016-2594-yen_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.sourceSpringer Berlin Heidelbergen_US
dc.titleAn Invariant of Topologically Ordered States Under Local Unitary Transformationsen_US
dc.typeArticleen_US
dc.identifier.citationHaah, Jeongwan. “An Invariant of Topologically Ordered States Under Local Unitary Transformations.” Communications in Mathematical Physics 342, no. 3 (February 22, 2016): 771–801.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Physicsen_US
dc.contributor.mitauthorHaah, Jeongwan
dc.relation.journalCommunications in Mathematical Physicsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-05-23T12:09:23Z
dc.language.rfc3066en
dc.rights.holderSpringer-Verlag Berlin Heidelberg
dspace.orderedauthorsHaah, Jeongwanen_US
dspace.embargo.termsNen
dc.identifier.orcidhttps://orcid.org/0000-0002-4420-4932
mit.licensePUBLISHER_POLICYen_US
mit.metadata.statusComplete


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