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Parafermionic conformal field theory on the lattice

Mong, Roger S. K. and Clarke, David J. and Alicea, Jason and Lindner, Netanel H. and Fendley, Paul (2014) Parafermionic conformal field theory on the lattice. Journal of Physics A: Mathematical and General, 47 (45). Art. No. 452001. ISSN 0305-4470. doi:10.1088/1751-8113/47/45/452001.

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Finding the precise correspondence between lattice operators and the continuum fields that describe their long-distance properties is a largely open problem for strongly interacting critical points. Here we solve this problem essentially completely in the case of the three-state Potts model, which exhibits a phase transition described by a strongly interacting 'parafermion' conformal field theory. Using symmetry arguments, insights from integrability, and extensive simulations, we construct lattice analogues of nearly all the relevant and marginal physical fields governing this transition. This construction includes chiral fields such as the parafermion. Along the way we also clarify the structure of operator product expansions between order and disorder fields, which we confirm numerically. Our results both suggest a systematic methodology for attacking non-free field theories on the lattice and find broader applications in the pursuit of exotic topologically ordered phases of matter.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Alicea, Jason0000-0001-9979-3423
Lindner, Netanel H.0000-0003-1879-3902
Additional Information:© 2014 IOP Publishing Ltd. Received 24 July 2014, revised 17 September 2014. Accepted for publication 19 September 2014. Published 27 October 2014. It is a pleasure to thank Erez Berg, Chetan Nayak, Miles Stoudenmire, and Mike Zaletel for helpful discussions related to this work. We also acknowledge funding from the NSF through grants DMR-1341822 (D. C. & J. A.) and DMR/MPS1006549 (P. F.) ; the Sherman Fairchild Foundation (R. M.) ; the Alfred P. Sloan Foundation (J. A.) ; the Bi-National Science Foundation and I-Core: the Israel Excellence Center ‘Circle of Light’ (N. L.) ; the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation; and the Walter Burke Institute for Theoretical Physics at Caltech. This work was completed at the Topological Phases and Quantum Computation Workshop 2014 under the hospitality of the Moorea Ecostation Center for Advanced Studies.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics at CaltechUNSPECIFIED
Subject Keywords:parafermions, conformal field theory, Potts model
Issue or Number:45
Classification Code:PACS: 11.25.Hf, 12.40.Ee, 64.60.F-. MSC:81T25, 81T40
Record Number:CaltechAUTHORS:20140715-151726687
Persistent URL:
Official Citation:Parafermionic conformal field theory on the lattice Roger S K Mong et al 2014 J. Phys. A: Math. Theor. 47 452001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:47237
Deposited By: Jacquelyn O'Sullivan
Deposited On:16 Jul 2014 15:53
Last Modified:12 Jul 2022 19:40

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