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

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 $3DZ_q$ 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 $β_{\rm{c}}(κ)$ which is first order for $κ$ below a finite {\it tricritical} value $κ_{\rm{tri}}$, 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 $(β_{\rm{tri}}, κ_{\rm{tri}}) = (1.23 \pm 0.03, 1.73 \pm 0.03)$. For all other integer $q \geq 2$ we have considered, the entire phase transition line $β_c(κ)$ is critical.