Exactly soluble models for fractional topological insulators in two and three dimensions

We construct exactly soluble lattice models for fractionalized, time-reversal-invariant electronic insulators in two and three dimensions. The low-energy physics of these models is exactly equivalent to a noninteracting topological insulator built out of fractionally charged fermionic quasiparticles. We show that some of our models have protected edge modes in two dimensions (2D) and surface modes (in 3D), and are thus fractionalized analogs of topological insulators. We also find that some of the 2D models do not have protected edge modes; that is, the edge modes can be gapped out by appropriate time-reversal-invariant, charge-conserving perturbations. (A similar state of affairs may also exist in 3D.) We show that all of our models are topologically ordered, exhibiting fractional statistics as well as ground-state degeneracy on a torus. In the 3D case, we find that the models exhibit a fractional magnetoelectric effect.