Braiding properties of paired spin-singlet and non-Abelian hierarchy states

Abstract

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 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.