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Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model

Tupitsyn, I. S. and Kitaev, A. and Prokof’ev, N. V. and Stamp, P. C. E. (2010) Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model. Physical Review B, 82 (8). Art. No. 085114. ISSN 1098-0121. doi:10.1103/PhysRevB.82.085114.

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We construct a mapping between the two-dimensional toric code model in external magnetic fields, h_z and h_x, and the three-dimensional classical Ising system with plaquette interactions, which is equivalent to the three-dimensional Z_2 gauge Higgs model with anisotropy between the imaginary time and spatial directions. The isotropic limit of the latter model was studied using Monte Carlo simulations on large (up to 60^3) lattices in order to determine the stability of the topological phase against generic magnetic field perturbations and to resolve fine details of the phase diagram. We find that the topological phase is bounded by second-order transition lines, which merge into a first-order line at what appears to be a multicritical point arising from the competition between the Higgs and confinement transitions in the Z_2 gauge system. An effective field theory for this type of multicritical point (if one actually exists) is not known. Our results have potential applications to frustrated magnets, quantum computation, lattice gauge models in particle physics, and critical phenomena.

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Additional Information:© 2010 The American Physical Society. Received 14 June 2010; published 17 August 2010. We thank E. Fradkin, B. Svistunov, S. Trebst, M. Troyer, I. Affleck, K. Shtengel, and S. Sachdev for discussions. We are also indebted to M. Berciu and J. Heyl whose research clusters were used to perform our MC simulations. N.P. acknowledges support from the National Science Foundation under Grant No. PHY-0653183, a grant from the Army Research Office with funding from the DARPA OLE program, and Aspen Center for physics.
Funding AgencyGrant Number
Army Research OfficeUNSPECIFIED
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Aspen Center for PhysicsUNSPECIFIED
Issue or Number:8
Classification Code:PACS: 05.50.+q, 03.65.Vf, 05.30.Pr, 05.70.Jk
Record Number:CaltechAUTHORS:20100907-152559860
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19810
Deposited By: Tony Diaz
Deposited On:08 Sep 2010 17:22
Last Modified:08 Nov 2021 23:55

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