Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect

Abstract

We present a method for the exact construction of the fully particle-hole symmetric PH-Pfaffian ground state and its charged excitations on a sphere. We adopt the Moore-Read state, but with a non- holomorphic pairing component as in previous studies, and project it to the lowest Landau level. We study the energetics as well as other properties of these states and find that in a pure system interact- ing with the Coulomb forces the PH-Pfaffian cannot compete with either the Moore-Read state or its particle-hole conjugate, the anti-Pfaffian state, as an explanation for the 5/2-effect.