| We present a solvable boson model with U(1)xfU(1) symmetry in (2+1) dimensions that realizes insulating phases with a quantized Hall conductivity σxy. The model is short-ranged, with no topological terms, and can be realized by a local Hamiltonian. For one set of parameters, the model has a non-fractionalized phase with σxy=2n in appropriate units, with n an integer. In this case, the physical origin is dynamical binding between n bosons of one species and a vortex of the other species and condensation of such composites. Other choices for the parameters of the model yield a phase with σxy=2c/d, where c and d are mutually prime integers. In this phase, c bosons dynamically bind to d vortices and such objects condense. The are two species of excitations that are bosonic by themselves but carry fractional charge 1/d and have mutual statistics 2*pi*b/d, where b is an integer such that ad-bc=1, and a is also an integer. The model can be studied using sign-free Monte Carlo. We have performed simulations which include a boundary between a quantum Hall insulator and a trivial insulator, and found gapless edge states on the boundary. |
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