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.
Highlights
The discovery of the fractional quantum Hall effect [1] has led to the prediction of fractionally charged quasiparticle excitations [2], quasiholes and quasielectrons, obeying fractional statistics [3, 4]
In this paper we have studied the braiding properties of the fundamental quasiholes in the paired spin-singlet states by finding explicit expressions of the quasihole wave functions and obtaining their monodromies
As expected on the basis of rank-level duality, we have shown that the non-abelian braiding properties of the quasiholes in the paired spin-singlet states are closely related to the quasiholes in the Read-Rezayi series, with the only difference an overall phase
Summary
The discovery of the fractional quantum Hall effect [1] has led to the prediction of fractionally charged quasiparticle excitations [2], quasiholes and quasielectrons, obeying fractional statistics [3, 4]. We study the manifest transformation properties of the paired spin-singlet states by obtaining explicit expressions for four-quasihole wave functions using conformal field theory techniques. This calculation relies on explicit four-point functions in certain Wess-Zumino-Witten (WZW) models which were obtained in Ref. The paired spin-singlet states are closely related to a set of non-abelian hierarchy wave functions proposed in [36] based on a picture of successive condensation of non-abelian quasiparticles This set of trial wave functions, which we refer to as Hermanns hierarchy wave functions, can be thought of as bilayer composite fermion wave functions where one performs a symmetrization (or antisymmetrization) over the layer index. We provide details on the WZW CFTs, the associated parafermion CFTs and the consequences of rank-level duality for the braid matrices studied in this paper
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