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

TL;DR

This study uses large-scale Monte Carlo simulations to analyze phase transitions in 3D compact abelian Higgs models with various matter representations, revealing the nature of phase transition lines and tricritical points.

Contribution

It provides the first detailed numerical analysis of phase transition lines and tricritical points in 3D compact abelian Higgs models for multiple matter field representations.

Findings

For q=3, the phase transition line changes from first to second order at a tricritical point.

The first order transition at infinite matter coupling persists at finite coupling.

For other q values, the phase transition line remains critical across the parameter space.

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 $(\beta,\kappa)$, where $\beta$ is the coupling constant of the matter term, and $\kappa$ 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 $\beta_{\rm{c}}(\kappa)$ which is first order for $\kappa$ below a finite {\it tricritical} value $\kappa_{\rm{tri}}$, and second order above. We have found that the $\beta=\infty$ first order phase transition persists for finite $\beta$ and joins the second order phase transition at a tricritical point $(\beta_{\rm{tri}}, \kappa_{\rm{tri}}) = (1.23 \pm 0.03, 1.73 \pm 0.03)$. For all other integer $q \geq 2$ we have considered, the entire phase transition line $\beta_c(\kappa)$ is critical.