Fractional Chiral Hinge Insulator

TL;DR

This paper introduces a model for a three-dimensional fractional chiral hinge insulator with fractional hinge modes, characterized by entanglement properties and topological degeneracy, using variational Monte Carlo methods.

Contribution

It constructs and analyzes a new fractional topological insulator model with fractional hinge modes and provides numerical evidence of its topological properties and degeneracies.

Findings

Fractional chiral hinge modes with central charge c=1 and Luttinger parameter K=1/2.

Observation of non-trivial topological degeneracy in the model.

Surface topological order with a topological entanglement entropy consistent with a Laughlin 1/2 state.

Abstract

We propose and study a wave function describing an interacting three-dimensional fractional chiral hinge insulator (FCHI) constructed by Gutzwiller projection of two non-interacting second order topological insulators with chiral hinge modes at half filling. We use large-scale variational Monte Carlo computations to characterize the model states via the entanglement entropy and charge-spin-fluctuations. We show that the FCHI possesses fractional chiral hinge modes characterized by a central charge $c=1$ and Luttinger parameter $K=1/2$, like the edge modes of a Laughlin $1/2$ state. By changing the boundary conditions for the underlying fermions, we investigate the topological degeneracy of the FCHI. Within the range of the numerically accessible system sizes, we observe a non-trivial topological degeneracy. A more numerically pristine characterization of the bulk topology is provided by the topological entanglement entropy (TEE) correction to the area law. While our computations indicate a vanishing bulk TEE, we show that the gapped surfaces host a two-dimensional topological order with a TEE per surface compatible with half that of a Laughlin $1/2$ state, a value that cannot be obtained from topological quantum field theory.