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Published July 9, 2012 | Published + Submitted
Journal Article Open

Phases and phase transitions in a U(1) × U(1) system with θ = 2π/3 mutual statistics

Abstract

We study a U(1) × U(1) system with short-range interactions and mutual θ = 2π/3 statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem and perform a Monte Carlo study. We find a phase diagram containing a phase with only small loops and two phases with one species of proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes. Lastly, when the energy cost of loops becomes small, we find a phase that is a condensate of bound states, each made up of three particles of one species and a vortex of the other. We define several exact reformulations of the model that allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic descriptions of the phases and phase transitions, which are particularly interesting on the "self-dual" line where both species have identical interactions. We also define irreducible responses useful for describing the phases.

Additional Information

© 2012 American Physical Society. Received 8 May 2012; published 9 July 2012. We are thankful to A. Vishwanath, M. P. A. Fisher, T. Senthil, R. Kaul, G. Murthy, J. Moore, N. Read, A. Shapere, and W. Witzak-Krempa for stimulating discussions. This research is supported by the National Science Foundation through grant DMR-0907145; by the Caltech Institute of Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation; and by the XSEDE computational initiative grant TG-DMR110052.

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Published - Geraedts2012p19023Phys_Rev_B.pdf

Submitted - 1205.1790v2.pdf

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