Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons

TL;DR

This paper introduces new model wavefunctions for non-Abelian quasielectron excitations in fractional quantum Hall states, using generalized clustering conditions, and explores their implications for hierarchy schemes and state properties.

Contribution

It defines unique quasielectron wavefunctions for non-Abelian FQH states via clustering conditions, differing from prior Jain constructions, and links to the Gaffnian state.

Findings

Reproduces Jain quasielectron wavefunction for Abelian states

Differentiates from Jain's method for multiple quasielectrons

Enables hierarchy construction leading to the Gaffnian state

Abstract

We present model wavefunctions for quasielectron (as opposed to quasihole) excitations of the unitary $Z_k$ parafermion sequence (Laughlin/Moore-Read/Read-Rezayi) of Fractional Quantum Hall states. We uniquely define these states through two generalized clustering conditions: they vanish when either a cluster of $k+2$ electrons is put together, or when two clusters of $k+1$ electrons are formed at different positions. For Abelian Fractional Quantum Hall states ($k=1$), our construction reproduces the Jain quasielectron wavefunction, and elucidates the difference between the Jain and Laughlin quasielectrons. For two (or more) quasielectrons, our states differ from those constructed using Jain's method. By adding our quasielectrons to the Laughlin state, we obtain a hierarchy scheme which gives rise the non-Abelian non-unitary $\nu={2/5}$ FQH Gaffnian state.