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.

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Condensate induced transitions between topologically ordered phases
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Fractional topological superconductors with fractionalized Majorana fermions
• Topological Quantum Compiling
• Parafermionic conformal field theory on the lattice
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Universal Gates via Fusion and Measurement Operations on SU$(2{)}_4$ Anyons
• Topological quantum computation within the anyonic system the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4