Monte Carlo Study of a U(1)xU(1) system with π-statistical Interaction

Abstract

We study a $U(1)\times U(1)$ system with two species of loops with mutual $\pi$-statistics in (2+1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength, and therefore avoid the statistical interactions. We study another model which does not have this phase, and also find first-order behavior on the self-dual segment.

4 pages, 5 figures

References in corpus (15)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Anyons and the quantum Hall effect - a pedagogical review
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Topological BF field theory description of topological insulators
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory
• Field- and temperature induced topological phase transitions in the three-dimensional $N$-component London superconductor
• Mutual Chern-Simons theory for Z_2 topological order
• Phase transitions in a three dimensional $U(1)\times U(1)$ lattice London superconductor: Metallic superfluid and charge-4e superconducting states
• Coulomb gas transitions in three-dimensional classical dimer models
• Unconventional continuous phase transition in a three dimensional dimer model
• First-order phase transition in easy-plane quantum antiferromagnets
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets

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