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

TL;DR

This paper develops an exact method to construct the PH-Pfaffian state in the fractional quantum Hall effect and finds it energetically unfavorable compared to other states like Moore-Read and anti-Pfaffian.

Contribution

It introduces a precise construction of the PH-Pfaffian state on a sphere and analyzes its energetics in Coulomb-interacting systems.

Findings

PH-Pfaffian state is not energetically favored over Moore-Read or anti-Pfaffian states

Method for constructing particle-hole symmetric states on a sphere

Analysis of energetics relevant to 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 nonholomorphic 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 interacting 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.