Fractional topological liquids with time-reversal symmetry and their lattice realization

TL;DR

This paper introduces a new class of two-dimensional, time-reversal-symmetric fractional topological liquids supporting fractionalized excitations, analyzes their edge state stability, and demonstrates their realization in a lattice model through numerical methods.

Contribution

It presents a novel class of fractional topological liquids with time-reversal symmetry, including a stability criterion for edge states and a lattice model realization studied via exact diagonalization.

Findings

Identification of a Z_2 stability criterion for edge states.

Evidence of fractional topological liquid phases in a lattice model.

Observation of a phase with quantized Hall conductance breaking time-reversal symmetry.

Abstract

We present a class of time-reversal-symmetric fractional topological liquid states in two dimensions that support fractionalized excitations. These are incompressible liquids made of electrons, for which the charge Hall conductance vanishes and the spin Hall conductance needs not be quantized. We then analyze the stability of edge states in these two-dimensional topological fluids against localization by disorder. We find a Z_2 stability criterion for whether or not there exists a Kramers pair of edge modes that is robust against disorder. We also introduce an interacting electronic two-dimensional lattice model based on partially filled flattened bands of a Z_2 topological band insulator, which we study using numerical exact diagonalization. We show evidence for instances of the fractional topological liquid phase as well as for a time-reversal symmetry broken phase with a quantized (charge) Hall conductance in the phase diagram for this model.