Exactly soluble models for fractional topological insulators in 2 and 3 dimensions

TL;DR

This paper develops exactly solvable lattice models for fractional topological insulators in 2D and 3D, revealing protected edge and surface modes, topological order, and fractional magnetoelectric effects.

Contribution

It introduces new exactly solvable models for fractional topological insulators that incorporate fractionalized quasiparticles and topological order, extending understanding of topological phases.

Findings

Some models have protected edge and surface modes.

All models exhibit topological order with fractional statistics.

3D models show fractional magnetoelectric effect.

Abstract

We construct exactly soluble lattice models for fractionalized, time reversal invariant electronic insulators in 2 and 3 dimensions. The low energy physics of these models is exactly equivalent to a non-interacting topological insulator built out of fractionally charged fermionic quasiparticles. We show that some of our models have protected edge modes (in 2D) and surface modes (in 3D), and are thus fractionalized analogues 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.