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Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting

E. Ardonne·N. Read·E. Rezayi·K. Schoutens
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Abstract

We investigate a class of non-Abelian spin-singlet (NASS) quantum Hall phases, proposed previously. The trial ground and quasihole excited states are exact eigenstates of certain k+1-body interaction Hamiltonians. The k=1 cases are the familiar Halperin Abelian spin-singlet states. We present closed-form expressions for the many-body wave functions of the ground states, which for k>1 were previously defined only in terms of correlators in specific conformal field theories. The states contain clusters of k electrons, each cluster having either all spins up, or all spins down. The ground states are non-degenerate, while the quasihole excitations over these states show characteristic degeneracies, which give rise to non-Abelian braid statistics. Using conformal field theory methods, we derive counting rules that determine the degeneracies in a spherical geometry. The results are checked against explicit numerical diagonalization studies for small numbers of particles on the sphere.

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E. Ardonne, N. Read, E. Rezayi, K. Schoutens. 2001-04-13. Non-Abelian spin-singlet quantum Hall states: wave functions and quasihole state counting. https://doi.org/10.1016/s0550-3213(01)00224-3

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