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Monte Carlo study of a U(1) × U(1) loop model with modular invariance

Geraedts, Scott D. and Motrunich, Olexei I. (2012) Monte Carlo study of a U(1) × U(1) loop model with modular invariance. Physical Review B, 86 (24). Art. No. 245121. ISSN 1098-0121. doi:10.1103/PhysRevB.86.245121.

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We study a U(1)×U(1) system in (2+1) dimensions with long-range interactions and mutual statistics. The model has the same form after the application of operations from the modular group, a property which we call modular invariance. Using the modular invariance of the model, we propose a possible phase diagram. We obtain a sign-free reformulation of the model and study it in Monte Carlo. This study confirms our proposed phase diagram. We use the modular invariance to analytically determine the current-current correlation functions and conductivities in all the phases in the diagram, as well as at special “fixed” points which are unchanged by an operation from the modular group. We numerically determine the order of the phase transitions, and find segments of second-order transitions. For the statistical interaction parameter θ=π, these second-order transitions are evidence of a critical loop phase obtained when both loops are trying to condense simultaneously. We also measure the critical exponents of the second-order transitions.

Item Type:Article
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Motrunich, Olexei I.0000-0001-8031-0022
Additional Information:© 2012 American Physical Society. Received 8 October 2012; published 19 December 2012. We are thankful to A. Vishwanath, M. P. A. Fisher, I. Gruzberg, A. Kitaev, N. Read, T. Senthil, and S. Simon for stimulating discussions. This research is supported by the National Science Foundation through Grants No. DMR-0907145 and No. DMR-1206096; 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 XSEDE Computational Initiative Grant No. TG-DMR110052.
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
Issue or Number:24
Classification Code:PACS: 64.60.De
Record Number:CaltechAUTHORS:20130122-074509815
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Official Citation:Monte Carlo study of a U(1)×U(1) loop model with modular invariance Scott D. Geraedts and Olexei I. Motrunich Published 19 December 2012 (13 pages) 245121
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36488
Deposited By: Ruth Sustaita
Deposited On:22 Jan 2013 16:32
Last Modified:09 Nov 2021 23:22

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