Monte Carlo study of phase transitions out of Symmetry-Enriched Topological phases of bosons in two dimensions

We study a statistical mechanics model of two species of bosons with mutual statistics $\theta =2\pi \mathrm{/}n$ in (2+1) dimensions. This model realizes a fractionalized topological phase of bosons, which is a fractionalized version of the boson integer quantum Hall effect. The model can be studied with sign-free Monte Carlo simulations. We study the phase transitions between the fractionalized topological phase and a trivial insulator, and between different topological phases. We find that these transitions are continuous, and we measure their critical exponents.