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

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 statistics are identical to those of Z${}_3$ Parafermions.

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Cited by in corpus (4)

• Qutrit Toric Code and Parafermions in Trapped Ions
• A Classical Algorithm for Quantum $\text{SU}(2)$ Schur Sampling
• Commuting-projector Hamiltonians for chiral topological phases built from parafermions
• Conformal field theory approach to parton fractional quantum Hall trial wave functions