Exclusion statistics for non-abelian quantum Hall states

TL;DR

This paper analyzes the exclusion statistics of edge quasi-particles in a non-abelian quantum Hall state, specifically the Pfaffian state at filling factor 1/2, revealing dualities and thermodynamic properties.

Contribution

It explicitly determines the exclusion statistics and thermodynamic distributions of edge excitations in the Pfaffian non-abelian quantum Hall state, extending fractional exclusion statistics concepts.

Findings

Derived thermodynamic distribution functions for edge quasi-particles.

Established a duality generalizing Haldane's fractional exclusion statistics.

Characterized the exclusion statistics of electrons and quasi-holes in the Pfaffian state.

Abstract

We determine the exclusion statistics properties of the fundamental edge quasi-particles over a specific $\nu=\half$ non-abelian quantum Hall state known as the pfaffian. The fundamental excitations are the edge electrons of charge $-e$ and the edge quasi-holes of charge $+{e \over 4}$. We explicitly determine thermodynamic distribution functions and establish a duality which generalizes the duality for fractional exclusion statistics in the sense of Haldane.