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

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.

4 pages 3 figures

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
• Paired composite fermion wavefunctions
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement
• Contrasting Behavior of the 5/2 and 7/3 Fractional Quantum Hall Effect in a Tilted Field
• Understanding the 5/2 Fractional Quantum Hall Effect without the Pfaffian Wave Function
• Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect

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