The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian

TL;DR

This study uses exact diagonalization to show that the nu=5/2 fractional quantum Hall state aligns with the Moore-Read wave function, indicating potential non-Abelian statistics, while the nu=1/2 state shows less conclusive evidence.

Contribution

It demonstrates the adiabatic connection between the Coulomb ground state at nu=5/2 and the Moore-Read state through pseudopotential variations.

Findings

Nu=5/2 state is well described by Moore-Read wave function.

Non-Abelian statistics are likely at nu=5/2.

Nu=1/2 state does not show clear Moore-Read phase in the thermodynamic limit.

Abstract

Results from exact diagonalization show that the spin-polarized Coulomb ground state at nu=5/2 is adiabatically connected with the Moore-Read wave function for systems with up to Nel = 16 electrons on the surface of a sphere. Varying the Haldane pseudopotentials v1 and v3, keeping all others at their value for Coulomb interaction, energy gap and (v1,v3)-dependent ground state overlap with the Moore-Read state form two ridges whose peak positions and extent in the (v1,v3)-plane essentially coincide. Thus, the physics of the Coulomb ground state at nu=5/2 is indeed captured by the Moore-Read state and that non-Abelian statistics can be expected under experimental conditions. Such adiabatic connection is not observed at nu=1/2, unless the width of the interface wave function and/or Landau level mixing effects are sufficiently large. Varying the width, an excitation gap is found for all system sizes Nel \le 18 studied. However, its system size dependence casts doubt on the existence of a Moore-Read-phase at nu=1/2 in the thermodynamic limit.