## How SU(2)$_4$ Anyons are Z$_3$ Parafermions

Richard Fern, Johannes Kombe, Steven H. Simon

SciPost Phys. 3, 037 (2017) · published 9 December 2017

### Abstract

We consider the braid group representation which describes the non-abelian braiding statistics of the spin $1/2$ particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding properties can be represented exactly using $\mathbb{Z}_3$ parafermion operators.

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