Non-abelian Exclusion Statistics

TL;DR

This paper introduces order-$k$ non-abelian exclusion statistics, deriving thermodynamic equations via the Thermodynamic Bethe Ansatz, connecting with conformal field theory, and applying to non-abelian quantum Hall states.

Contribution

It presents a new framework for non-abelian exclusion statistics, deriving thermodynamic equations and linking them to conformal field theory and quantum Hall applications.

Findings

Derived thermodynamic distribution functions for non-abelian quantum Hall quasi-holes.

Established connections between non-abelian exclusion statistics and fermionic sum formulas.

Validated the thermodynamic equations with existing results.

Abstract

We introduce the notion of `order-$k$ non-abelian exclusion statistics'. We derive the associated thermodynamic equations by employing the Thermodynamic Bethe Ansatz for specific non-diagonal scattering matrices. We make contact with results obtained by different methods and we point out connections with `fermionic sum formulas' for characters in a Conformal Field Theory. As an application, we derive thermodynamic distribution functions for quasi-holes over a class of non-abelian quantum Hall states recently proposed by Read and Rezayi.