Characterization of quasiholes in fractional Chern insulators

TL;DR

This paper investigates the properties of quasiholes in fractional Chern insulators, relating their density distribution and size to fractional quantum Hall states, and confirms their fractional statistics through braiding simulations.

Contribution

It establishes a method to predict quasihole sizes in fractional Chern insulators based on fractional quantum Hall states and analyzes their braiding statistics.

Findings

Quasihole density distribution in Chern insulators relates to quantum Hall states.

Quasihole size depends on lattice model and can be predicted.

Braiding phases match theoretical fractional statistics predictions.

Abstract

We provide a detailed study of the Abelian quasiholes of $\nu=1/2$ bosonic fractional quantum Hall states on the torus geometry and in fractional Chern insulators. We find that the density distribution of a quasihole in a fractional Chern insulator can be related to that of the corresponding fractional quantum Hall state by choosing an appropriate length unit on the lattice. This length unit only depends on the lattice model that hosts the fractional Chern insulator. Therefore, the quasihole size in a fractional Chern insulator can be predicted for any lattice model once the quasihole size of the corresponding fractional quantum Hall state is known. We discuss the effect of the lattice embedding on the quasihole size. We also perform the braiding of quasiholes for fractional Chern insulator models to probe the fractional statistics of these excitations. The numerical values of the braiding phases accurately match the theoretical predictions.