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

Understand

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.