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Published July 2013 | Submitted
Journal Article Open

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

Abstract

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.

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''.

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August 22, 2023
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