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Anyons are not energy eigenspaces of quantum double Hamiltonians

Kómár, Anna and Landon-Cardinal, Olivier (2017) Anyons are not energy eigenspaces of quantum double Hamiltonians. Physical Review B, 96 (19). Art. No. 195150. ISSN 2469-9950. https://resolver.caltech.edu/CaltechAUTHORS:20170605-083553920

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Abstract

Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a two-dimensional spin lattice. Their Hamiltonian defines the ground space by imposing an energy penalty to any nontrivial flux or charge, but does not distinguish among those. We generalize this construction by introducing a family of Hamiltonians made of commuting four-body projectors that provide an intricate splitting of the Hilbert space by discriminating among nontrivial charges and fluxes. Our construction highlights that anyons are not in one-to-one correspondence with energy eigenspaces, a feature already present in Kitaev's construction. This discrepancy is due to the presence of local degrees of freedom in addition to topological ones on a lattice.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.96.195150DOIArticle
https://arxiv.org/abs/1701.04456arXivDiscussion Paper
Alternate Title:Tunable excitation spectrum in quantum double models
Additional Information:© 2017 American Physical Society. Received 16 June 2017; published 27 November 2017. We thank J. Preskill, A. Kitaev, D. Aasen, B. Levitan, S. Shukla, and D. Williamson for helpful discussions. We acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1125565) with support of the Gordon and Betty Moore Foundation (Grant No. GBMF-2644). O.L.C. is partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Issue or Number:19
Record Number:CaltechAUTHORS:20170605-083553920
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170605-083553920
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77936
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jun 2017 21:30
Last Modified:03 Oct 2019 18:03

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