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

Michael Levin, F. J. Burnell, MacIej Koch-Janusz, Ady Stern

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Abstract

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.

Original languageEnglish (US)
Article number235145
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume84
Issue number23
DOIs
StatePublished - Dec 27 2011

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