# Braiding properties of paired spin-singlet and non-abelian hierarchy states

## TL;DR

This paper investigates the braiding statistics of quasiholes in a family of non-abelian fractional quantum Hall states, revealing their monodromy properties and connections to Read-Rezayi states, with implications for non-abelian hierarchy wave functions.

## Contribution

It explicitly determines the braid statistics of quasiholes in paired spin-singlet non-abelian states and relates them to known Read-Rezayi states, advancing understanding of their topological properties.

## Key findings

- Quasiholes exhibit the same braid statistics as Read-Rezayi quasiholes, up to a phase.
- Explicit wave functions allow calculation of monodromy and braiding properties.
- Results apply to a class of non-abelian hierarchy wave functions.

## Abstract

We study explicit model wave functions describing the fundamental quasiholes in a class of non-abelian fractional quantum Hall states. This class is a family of paired spin-singlet states with $n\geq1$ internal degrees of freedom. We determine the braid statistics of the quasiholes by determining the monodromy of the explicit quasihole wave functions, that is how they transform under exchanges of quasihole coordinates. The statistics is shown to be the same as that of the quasiholes in the Read-Rezayi states, up to a phase. We also discuss the application of this result to a class of non-abelian hierarchy wave functions.