Edge Excitations in Fractional Chern Insulators

TL;DR

This paper provides numerical evidence of chiral edge excitations in fractional Chern insulators, supporting their topological nature and potential for experimental detection without external magnetic fields.

Contribution

It offers the first exact numerical analysis of edge excitations in fractional Chern insulators on disk geometries, confirming chiral Luttinger liquid behavior.

Findings

Edge excitations match chiral Luttinger liquid theory

Edge states are present in honeycomb and kagome lattice models

Edge states are verified by flux insertion tests

Abstract

Recent theoretical works have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role to obtain a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagom\'{e}-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.