The Second Landau Level Projection of Antiholomorphic Pfaffian Wavefunctions

TL;DR

This paper introduces a new gapped quantum Hall state called the SLL PH-Pfaffian, derived from the second Landau level projection of an antiholomorphic Pfaffian wavefunction, which closely matches the exact ground state and shares topological features with the anti-Pfaffian.

Contribution

The paper proposes the SLL PH-Pfaffian state, a novel second Landau level wavefunction with antiholomorphic pairing, providing a better description of the ground state in certain quantum Hall systems.

Findings

The SLL PH-Pfaffian is a gapped, incompressible phase.

It has high overlap with the exact ground state of Coulomb-interacting electrons.

It shares low-energy entanglement spectrum features with the anti-Pfaffian.

Abstract

We propose a new state described by the second Landau level (SLL) projection of a generalized Moore-Read Pfaffian wavefunction with an antiholomorphic pairing component. Unlike the PH-Pfaffian state which is described by the lowest Landau level (LLL) projection of the same antiholomorphic Pfaffian wavefunction, we find the proposed state, which we call the SLL PH-Pfaffian, represents a gapped, incompressible phase, and provides an excellent description for the exact ground state of finite-size SLL Coulomb-interacting electrons over a range of the short distance interaction strength. We also find the SLL PH-Pfaffian, when mapped to the LLL, has a very large overlap and the same low-energy orbital entanglement spectrum structures with the anti-Pfaffian state. We discuss possible interpretations of our results on the nature of the topological order of both states.