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Exact realization of Integer and Fractional Quantum Hall Phases in U(1) × U(1) models in (2 + 1)d

Geraedts, Scott D. and Motrunich, Olexei I. (2013) Exact realization of Integer and Fractional Quantum Hall Phases in U(1) × U(1) models in (2 + 1)d. Annals of Physics, 334 . pp. 288-315. ISSN 0003-4916. doi:10.1016/j.aop.2013.03.017.

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In this work we present a set of microscopic U(1) × U(1) models which realize insulating phases with a quantized Hall conductivity σ_(xy). The models are defined in terms of physical degrees of freedom, and can be realized by local Hamiltonians. For one set of these models, we find that σ_(xy) is quantized to be an even integer. The origin of this effect is a condensation of objects made up of bosons of one species bound to a single vortex of the other species. For other models, the Hall conductivity can be quantized as a rational number times two. For these systems, the condensed objects contain bosons of one species bound to multiple vortices of the other species. These systems have excitations carrying fractional charges and non-trivial mutual statistics. We present sign-free reformulations of these models which can be studied in Monte Carlo, and we use such reformulations to numerically detect a gapless boundary between the quantum Hall and trivial insulator states. We also present the broader phase diagrams of the models.

Item Type:Article
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Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2013 Elsevier Inc. Received 26 February 2013; Accepted 29 March 2013; Available online 12 April 2013. We would like to thank M.P.A. Fisher, A. Kitaev, T. Senthil, and A. Vishwanath, whose penetrating questions and suggestions inspired much of this work. We also thank J. Alicea and A. Kapustin for useful discussions. This research is supported by the National Science Foundation through grant DMR-1206096, and by the Caltech Institute of Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation. SG is supported by an NSERC PGS fellowship. OIM would also like to acknowledge fruitful participation in the KITP program ‘‘Exotic Phases of Frustrated Magnets’’.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Topological insulator; Symmetry Protected Topological phase
Record Number:CaltechAUTHORS:20130719-143804802
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Official Citation:Scott D. Geraedts, Olexei I. Motrunich, Exact realization of integer and fractional quantum Hall phases in models in, Annals of Physics, Volume 334, July 2013, Pages 288-315, ISSN 0003-4916,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39473
Deposited By: Tony Diaz
Deposited On:22 Jul 2013 21:03
Last Modified:09 Nov 2021 23:45

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