Phases and phase transitions in aU(1)×U(1)system withθ=2π/3

Abstract

We study a U (1) × U (1) system with short-range interactions and mutual θ = 2π/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 fieldtheoretic 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.

Lattice realization of a bosonic integer quantum Hall state–trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model

“…We support this phase diagram by summarizing a number of previous Monte Carlo studies. 12,[27][28][29] Finally in Sec. V we explicitly show how the model is connected to the EP-NCCP1 model, and also how it connects to the model studied numerically in Ref.…”

“…(32), and also an exact reformulation of the easy-plane NCCP1 model, where a symmetry under the interchange of the two species with mutual π statistics corresponds to the exact self-duality of the EP-NCCP1 model. 27,28 Here we simply state the numerical results of Ref. 27, which are that there is a phase transition along the λ 1 = λ 2 line and that the phase transition is weakly first-order.…”

“…Our model has two species of separately conserved bosons with short-range interactions that break conventional time-reversal symmetry but preserve an alternate antiunitary symmetry that allows a sign-free reformulation and Monte Carlo studies already employed in previous works. 12,[27][28][29] Both species are at integer filling due to an additional local unitary particle-hole symmetry, which however is not an obstacle to producing BIQHE or its fractionalized cousins, i.e., "symmetry-enriched topological phases" (SET). We then show that requiring an interchange symmetry between the two boson species is crucial for realizing the direct transition between the BIQHE and trivial phase.…”

Loop models, modular invariance, and three-dimensional bosonization

“…4 These issues with modular invariance do not arise in models consisting of two species of loops which can only statistically interact with one another. Such models display modular invariance and may be related to BF theories in the continuum limit [44][45][46]. and review the appearance of PSL(2, Z) in both contexts.…”

Anyon Condensation and Its Applications

“…The more experimentally relevant Hamiltonian realizations of TSB involve bilayer quantum Hall systems, [78][79][80]82,113 78,130 and a bilayer of the Moore-Read state. 76,113 However, to study the critical point in a systematic way it is advantageous to use more tractable (but less physically realistic) lattice models, 42,60,76,77,84,86,129,[131][132][133][134][135][136][137][138] which will be our focus here. Tensor-network constructions 58,139 provide an alternative, wave-function based, approach to TSB on the lattice.…”