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Emergent photons and transitions in the O(3) sigma model with hedgehog suppression

Motrunich, Olexei I. and Vishwanath, Ashvin (2004) Emergent photons and transitions in the O(3) sigma model with hedgehog suppression. Physical Review B, 70 (7). Art. No. 075104. ISSN 1098-0121. doi:10.1103/PhysRevB.70.075104.

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We study the effect of hedgehog suppression in the O(3) sigma model in D = 2 + 1. We show via Monte Carlo simulations that the sigma model can be disordered while effectively forbidding these point topological defects. The resulting paramagnetic state has gauge charged matter with half-integer spin (spinons) and also an emergent gauge field (photons), whose existence is explicitly demonstrated. Hence, this is an explicit realization of fractionalization in a model with global SU(2) symmetry. The zero-temperature ordering transition from this phase is found to be continuous but distinct from the regular Heisenberg ordering transition. We propose that these phases and this phase transition are captured by the noncompact CP1 model, which contains a pair of bosonic fields coupled to a noncompact U(1) gauge field. Direct simulation of the transition in this model yields critical exponents that support this claim. The easy-plane limit of this model also displays a continuous zero temperature ordering transition, which has the remarkable property of being self-dual. The presence of emergent gauge charge and hence Coulomb interactions is evidenced by the presence of a finite temperature Kosterlitz-Thouless transition associated with the thermal ionization of the gauge charged spinons. Generalization to higher dimensions and the effects of nonzero hedgehog fugacity are discussed.

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Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:©2004 The American Physical Society (Received 13 January 2004; published 17 August 2004) We thank L. Balents, T. Senthil, S. Minwalla, and S. Sachdev for stimulating discussions, and D.A. Huse for useful suggestions and for generously sharing with us his unpublished work. We are especially grateful to M.P.A. Fisher for several vital conversations at the beginning of this project and for his encouragement throughout. O.I.M. was supported by the National Science Foundation under Grants No. DMR-0213282 and DMR–0201069. A.V. would like to acknowledge support from Pappalardo.
Subject Keywords:photons; Monte Carlo methods; gauge field theory; SU(2) theory; Heisenberg model; Kosterlitz-Thouless transition; ionisation; CP invariance
Issue or Number:7
Record Number:CaltechAUTHORS:MOTprb04c
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7112
Deposited By: Archive Administrator
Deposited On:09 Jan 2007
Last Modified:08 Nov 2021 20:39

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