Non-abelian spin-singlet quantum Hall states: wave functions and quasiholestate counting

We investigate a class of non-abelian spin-singlet (NASS) quantum Hall phas es, 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 stat es, which for k > 1 were previously defined only in terms of correlators in specific conformal field theories. The states contain clusters of k electr ons, each cluster having either all spins up, or all spins down. The ground states are non-degenerate, while the quasihole excitations over these stat es show characteristic degeneracies, which give rise to non-abelian braid s tatistics. Using conformal field theory methods, we derive counting rules t hat determine the degeneracies in a spherical geometry. The results are che cked against explicit numerical diagonalization studies for small numbers o f particles on the sphere. (C) 2001 Elsevier Science B.V. All rights reserv ed.