Fractional quantum Hall state at nu=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.
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Condensed Matter Theory, Paul Scherrer Institute, CH-5232 Villigen, Switzerland.
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Das Sarma
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