TY - JOUR
T1 - Exactly soluble models for fractional topological insulators in two and three dimensions
AU - Levin, Michael
AU - Burnell, F. J.
AU - Koch-Janusz, MacIej
AU - Stern, Ady
PY - 2011/12/27
Y1 - 2011/12/27
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevB.84.235145
DO - 10.1103/PhysRevB.84.235145
M3 - Article
AN - SCOPUS:84855394406
VL - 84
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
SN - 1098-0121
IS - 23
M1 - 235145
ER -