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Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level

N. Read·E. Rezayi
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Abstract

The Pfaffian quantum Hall states, which can be viewed as involving pairing either of spin-polarized electrons or of composite fermions, are generalized by finding the exact ground states of certain Hamiltonians with k+1-body interactions, for all integers k > 0. The remarkably simple wavefunctions of these states involve clusters of k particles, and are related to correlators of parafermion currents in two-dimensional conformal field theory. The k=2 case is the Pfaffian. For k > 1, the quasiparticle excitations of these systems are expected to possess nonabelian statistics, like those of the Pfaffian. For k=3, these ground states have large overlaps with the ground states of the (2-body) Coulomb-interaction Hamiltonian for electrons in the first excited Landau level at total filling factors ν=2+3/5, 2+2/5.

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N. Read, E. Rezayi. 1998-10-06. Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level. https://doi.org/10.1103/physrevb.59.8084

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