Contributor info: Mr Richard Fern

Richard Fern, Johannes Kombe, Steven H. Simon

SciPost Phys. 3, 037 (2017) · published 9 December 2017 | Toggle abstract · pdf

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.