Fractional Quantum Hall State at ν=5/2 and the Moore-Read Pfaffian

Using exact diagonalization we 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 18 electrons on the surface of a sphere. The ground state is protected by a large gap for all system sizes studied. Furthermore, varying the Haldane pseudopotentials v(1) and v(3), keeping all others at their value for the Coulomb interaction, energy gap and overlap between ground-and Moore-Read state form hills whose positions and extent in the (v(1), v(3)) plane coincide. We conclude that the physics of the Coulomb ground state at nu = 5/2 is captured by the Moore-Read state. Such an adiabatic connection is not found at nu = 1/2, unless the width of the interface wave function or Landau level mixing effects are large enough. Yet, a Moore-Read-phase at nu = 1/2 appears unlikely in the thermodynamic limit.