Anyon braiding in semi-analytical fractional quantum Hall lattice models

TL;DR

This paper introduces semi-analytical lattice models for fractional quantum Hall states using conformal field theory, enabling direct study of anyon braiding, structure, and dynamics in lattice systems.

Contribution

It develops explicit semi-analytical models for fractional quantum Hall states on lattices, allowing direct analysis of anyon properties and braiding in these systems.

Findings

Confirmed braiding properties match analytical predictions

Computed anyon size, charge, and internal structure

Analyzed anyon behavior near edges and under lattice effects

Abstract

It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this problem by using conformal field theory to build semi-analytical fractional quantum Hall lattice models having anyons in their ground states, and I carry out the construction explicitly for the family of bosonic and fermionic Laughlin states. This enables me to show directly that the braiding properties of the anyons are those expected from analytical continuation of the wave functions and to compute properties such as internal structure, size, and charge of the anyons with simple Monte Carlo simulations. The models can also be used to study how the anyons behave when they approach or even pass through the edge of the sample. Finally, I compute the effective magnetic field seen by the anyons, which varies periodically due to the presence of the lattice.