Parton construction of a wave function in the anti-Pfaffian phase

TL;DR

This paper introduces a parton wave function candidate for the anti-Pfaffian phase in the fractional quantum Hall effect, demonstrating its overlap with known states and its computational advantages for large systems.

Contribution

The authors propose a new parton wave function for the anti-Pfaffian phase, showing its phase equivalence and computational benefits over previous models.

Findings

High overlap with anti-Pfaffian state

Lies in same phase as anti-Pfaffian according to entanglement spectrum

Can be evaluated for large systems

Abstract

In this work we propose a parton state as a candidate state to describe the fractional quantum Hall effect in the half-filled second Landau level. The wave function for this parton state is $\mathcal{P}_{\rm LLL} \Phi_{1}^3[\Phi_{2}^{*}]^{2}\sim\Psi^{2}_{2/3}/\Phi_{1}$ and in the spherical geometry it occurs at the same flux as the anti-Pfaffian state. This state has a good overlap with the anti-Pfaffian state and with the ground state obtained by exact diagonalization, using the second Landau level Coulomb interaction pseudopotentials for an ordinary semiconductor such as GaAs. By calculating the entanglement spectrum we show that this state lies in the same phase as the anti-Pfaffian state. A major advantage of this parton state is that its wave function can be evaluated for large systems, which makes it amenable to variational calculations. In the appendix of this work we have numerically assessed the validity of another candidate state at filling factor $\nu=5/2$, namely the particle-hole-symmetric Pfaffian (PH-Pfaffian) state. We find that the proposed candidate wave function for the PH-Pfaffian state is particle-hole symmetric to a high degree but it does not appear to arise as the ground state of any simple Hamiltonian with two-body interactions.