Unified approach to quasi-particle excitations in the edge states of paired Hall states

Abstract

We consider the edge states of the quantum Hall paired states, which were introduced as the ground-state wave function for $\ensuremath{\nu}=\frac{5}{2}.$ We propose that the paired Hall states such as the Haldane-Rezayi state and the Pfaffian state have the supersymmetry, and we clarify the exclusion statistics of the quasi-particle excitations. By use of an idea of the ``restricted partition function'' for the quasi-particle excitations and its relationship with the q-special functions, we explicitly compute the distribution functions for the quasi-particle. We also calculate the specific heat and show that our results coincide with previously reported results based on the conformal field theory. We further show that there is a duality between the Pfaffian state and the Haldane-Rezayi state.