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

TL;DR

This paper investigates a complex $U(1)\times U(1)$ system with mutual statistics, revealing a rich phase diagram with various condensed and bound states, using reformulations that enable Monte Carlo simulations without sign problems.

Contribution

The study introduces exact reformulations of the model, enabling detailed Monte Carlo analysis and proposes field-theoretic descriptions of the phases and transitions.

Findings

Identified phases with small loops, proliferated loops, and bound states.

Discovered a phase with condensates of bound states of particles and vortices.

Provided precise descriptions of phases via gapped excitations and responses.

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.