Phase Structure of d=2+1 Compact Lattice Gauge Theories and the Transition from Mott Insulator to Fractionalized Insulator

J. Smiseth; E. Smoergrav; F. S. Nogueira; J. Hove; A. Sudbo

doi:10.1103/PhysRevB.67.205104

paper

Phase Structure of d=2+1 Compact Lattice Gauge Theories and the Transition from Mott Insulator to Fractionalized Insulator

arXiv:cond-mat/0301297 · doi:10.1103/PhysRevB.67.205104

Abstract

Large-scale Monte Carlo simulations are employed to study phase transitions in the three-dimensional compact abelian Higgs model in adjoint representations of the matter field, labelled by an integer q, for q=2,3,4,5. We also study various limiting cases of the model, such as the $Z_{q}$ lattice gauge theory, dual to the $3 D Z_{q}$ spin model, and the 3DXY spin model which is dual to the $Z_{q}$ lattice gauge theory in the limit $q \to \infty$ . We have computed the first, second, and third moments of the action to locate the phase transition of the model in the parameter space $(β, κ)$ , where $β$ is the coupling constant of the matter term, and $κ$ is the coupling constant of the gauge term. We have found that for q=3, the three-dimensional compact abelian Higgs model has a phase-transition line $β_{c} (κ)$ which is first order for $κ$ below a finite {\it tricritical} value $κ_{tri}$ , and second order above. We have found that the $β = \infty$ first order phase transition persists for finite $β$ and joins the second order phase transition at a tricritical point $(β_{tri}, κ_{tri}) = (1.23 \pm 0.03, 1.73 \pm 0.03)$ . For all other integer $q \geq 2$ we have considered, the entire phase transition line $β_{c} (κ)$ is critical.

arXiv comment17 pages, 12 figures (new Fig. 2), new Section IVB, updated references, submitted to Physical Review B

Phase Structure of d=2+1 Compact Lattice Gauge Theories and the Transition from Mott Insulator to Fractionalized Insulator

Abstract

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