$\mathbb Z_2$ fractional topological insulators in two dimensions

摘要

We propose a simple microscopic model to numerically investigate thestability of a two dimensional fractional topological insulator (FTI). Thesimplest example of a FTI consists of two decoupled copies of a Laughlin statewith opposite chiralities. We focus on bosons at half filling. We study thestability of the FTI phase upon addition of two coupling terms of differentnature: an interspin interaction term, and an inversion symmetry breaking termthat couples the copies at the single particle level. Using exactdiagonalization and entanglement spectra, we numerically show that the FTIphase is stable against both perturbations. We compare our system to a similarbilayer fractional Chern insulator. We show evidence that the time reversalinvariant system survives the introduction of interaction coupling on a largerscale than the time reversal symmetry breaking one, stressing the importance oftime reversal symmetry in the FTI phase stability. We also discuss possiblefractional phases beyond $\nu = 1/2$.