Spin-$S$ generalization of fractional exclusion statistics

TL;DR

This paper extends fractional exclusion statistics to quantum systems with arbitrary spin S, linking it to SU(2) symmetry, WZW models, and non-abelian quantum Hall states, providing a unified theoretical framework.

Contribution

It generalizes thermodynamic equations for fractional exclusion statistics to systems with arbitrary spin S, connecting them to WZW models and non-abelian quantum Hall states.

Findings

Describes the system using level-2S WZW model.

Links fractional exclusion statistics to non-abelian fractional quantum Hall states.

Extracts the massless Z_{2S} parafermion sector as a low-energy effective theory.

Abstract

We study fractional exclusion statistics for quantum systems with SU(2) symmetry (arbitrary spin $S$), by generalizing the thermodynamic equations with squeezed strings proposed by Ha and Haldane. The bare hole distributions as well as the statistical interaction defined by an infinite-dimensional matrix specify the universality class. It is shown that the system is described by the level-$2S$ WZW model and has a close relationship to non-abelian fractional quantum Hall states. As a low-energy effective theory, the sector of {\it massless} Z$_{2S}$ parafermions is extracted, whose statistical interaction is given by a finite-dimensional matrix.