Non-abelian spin-singlet quantum Hall states: wave functions and quasihole state counting |
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Institution: | 1. Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China;2. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210046, People’s Republic of China |
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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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