Phases and phase transitions in a $U(1)\times U(1)$ system with $\theta =2\pi /3$ mutual statistics

Abstract

We study a $U(1)\times U(1)$ system with short-range interactions and mutual $\theta =2\pi /3$ statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem, and perform a Monte Carlo study. We find a phase diagram containing a phase with only small loops and two phases with one species of proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes. Lastly, when the energy cost of loops becomes small we find a phase which is a condensate of bound states, each made up of three particles of one species and a vortex of the other. We define several exact reformulations of the model, which allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic descriptions of the phases and phase transitions, which are particularly interesting on the "self-dual" line where both species have identical interactions. We also define irreducible responses useful for describing the phases.

15 pages, 13 figures

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• Monte Carlo Study of a $U(1)\times U(1)$ Loop Model with Modular Invariance
• Monte Carlo study of phase transitions out of Symmetry-Enriched Topological phases of bosons in two dimensions
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter
• Geometric and computational aspects of chiral topological quantum matter