K-matrices for non-abelian quantum Hall states

TL;DR

This paper reveals a duality linking electron pairing and non-abelian statistics in quantum Hall states through K-matrices that describe exclusion statistics, enhancing understanding of these complex quantum systems.

Contribution

It introduces a duality relation connecting pairing and non-abelian statistics via K-matrices in quantum Hall states, providing a new framework for analyzing these phenomena.

Findings

K-matrices encode exclusion statistics of excitations

Duality relation links pairing and non-abelian statistics

Applicable to q-pfaffian and related quantum Hall states

Abstract

Two fundamental aspects of so-called non-abelian quantum Hall states (the q-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian statistics of the quasi-hole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.