Model of statistically coupled chiral fields on the circle

TL;DR

This paper develops a field theoretical model of multicomponent anyons with mutual statistical interactions, representing fractional exclusion statistics on a circle, and relates it to edge states in fractional quantum Hall systems.

Contribution

It introduces a free-form, bosonized model of coupled chiral fields with a symmetric statistics matrix, connecting fractional exclusion statistics to quantum Hall edge excitations.

Findings

Model captures fractional exclusion statistics with a symmetric matrix g_{αβ}.

Provides a bosonized form linking to quantum Hall edge states.

Relates statistical interactions to low-energy edge excitations.

Abstract

Starting from a field theoretical description of multicomponent anyons with mutual statistical interactions in the lowest Landau level, we construct a model of interacting chiral fields on the circle, with the energy spectrum characterized by a symmetric matrix $g_{\alpha\beta}$ with nonnegative entries. Being represented in a free form, the model provides a field theoretical realization of (ideal) fractional exclusion statistics for particles with linear dispersion, with $g_{\alpha\beta}$ as a statistics matrix. We derive the bosonized form of the model and discuss the relation to the effective low-energy description of the edge excitations for abelian fractional quantum Hall states in multilayer systems.