Significant insights into non-Abelian quantum Hall states are obtained from studying special multiparticle interaction Hamiltonians, whose unique ground states are the Moore-Read and Read-Rezayi states for the case of spinless electrons. We generalize this approach to include the electronic spin-$1/2$ degree of freedom. We demonstrate that in the absence of Zeeman splitting, the ground states of such Hamiltonians have large degeneracies and very rich spin structures. The spin structure of the ground states and low-energy excitations can be understood based on an emergent SU(3) symmetry for the case corresponding to the Moore-Read state. These states with different spin quantum numbers represent non-Abelian quantum Hall states with different magnetizations, whose quasihole properties are likely to be similar to those of their spin-polarized counterparts.

• Received 29 May 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.216808