Bridge between Abelian and Non-Abelian Fractional Quantum Hall States

TL;DR

This paper introduces a scheme to unify Abelian and non-Abelian fractional quantum Hall states using K-component Halperin wave functions, with numerical evidence supporting its effectiveness in one-component systems.

Contribution

It presents a novel method to construct and unify Abelian and non-Abelian quantum Hall states from K-component wave functions with symmetrization.

Findings

Numerical calculations support the unification scheme.

The scheme effectively models one-component quantum Hall systems.

It provides a framework connecting Abelian and non-Abelian states.

Abstract

We propose a scheme to construct the most prominent Abelian and non-Abelian fractional quantum Hall states from K-component Halperin wave functions. In order to account for a one-component quantum Hall system, these SU(K) colors are distributed over all particles by an appropriate symmetrization. Numerical calculations corroborate the picture that the proposed scheme allows for a unification of both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.