The ν=5/2 quantum Hall state revisited: spontaneous breaking of the chiral fermion parity and phase transition between Abelian and non-Abelian statistics

Abstract

We review a recent development in the theoretical understanding of the ν=5/2 quantum Hall plateau and propose a new conformal field theory, slightly different from the Moore–Read one, to describe another universality class relevant for this plateau. The ground state is still given by the Pfaffian and is completely polarized, however, the elementary quasiholes are charge 1/2 anyons with Abelian statistics θ= π/2, which obey complete spin–charge separation. The physical hole is represented by two such quasiholes plus a free neutral Majorana fermion. We also compute the periods and amplitudes of the chiral persistent currents in both states and show that they have different temperature dependence. Finally, we find indications of a classical two-step phase transition between the new and the Moore–Read states, through a compressible state, which is characterized by the spontaneous breaking of a hidden Z 2 symmetry corresponding to the conservation of the chiral fermion parity. We believe that this transition could explain the “kink” observed in the activation experiment for ν=5/2.