Fractional Quantum Hall States with Non Abelian Statistics

G. Möllera, A. Wójsa, b and N.R. Coopera a TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK b Institute of Physics, Wrocław University of Technology, Wrocław, Poland

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Using exact numerical diagonalization we have studied correlated many electron ground states in a partially filled second Landau level. We consider filling fractions ν = 1/2 and 2/5, for which incompressible quantum liquids with non Abelian anion statistics have been proposed. Our calculations include finite layer width, Landau level mixing and arbitrary deformation of the interaction pseudopotential. Computed energies, gaps, and correlation functions support the non Abelian ground states at both ν = 1/2 ("Pfaffian") and ν = 2/5 ("parafermion" state).

DOI: 10.12693/APhysPolA.116.847 PACS numbers: 73.43.-f, 71.10.Pm