Particle-hole symmetry and the pfaffian state

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a ν=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed σxy=52(e2/h) quantum Hall plateau.