A nu=2/5 Paired Wavefunction

TL;DR

This paper constructs a new wavefunction for spinless electrons at filling fraction 2/5, generalizing the Moore-Read Pfaffian, and explores its properties including quasihole degeneracies and potential experimental relevance.

Contribution

It introduces a novel wavefunction based on a non-unitary conformal field theory for the 2/5 state, revealing its critical nature and quasihole zero-modes.

Findings

Wavefunction has high overlap with exact diagonalizations.

Quasiholes exhibit semionic statistics.

Wavefunction describes a quantum critical state.

Abstract

We construct a wavefunction, generalizing the well known Moore-Read Pfaffian, that describes spinless electrons at filling fraction nu=2/5 (or bosons at filling fraction nu=2/3) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero-modes of the quasiholes. The zero-modes are identified as having semionic statistics. We write this wavefunction as a correlator of the Virasoro minimal model conformal field theory M(5,3). Since this model is non-unitary, we conclude that this wavefunction is a quantum critical state. Nonetheless, we find that the overlaps of this wavefunction with exact diagonalizations in the lowest and first excited Landau level are very high, suggesting that this wavefunction may have experimental relevance for some transition that may occur in that regime.