We propose and analyze two series of clustered quantum Hall states for rotating systems of spin-1 bosons. The first series [labeled SU(4)(k)] includes the exact ground states of a model Hamiltonian at large angular momentum L, and also for N=3k particles at L=N. The latter is a spin-singlet boson-triplet condensate. The second series, labeled SO(5)(k), includes exact ground states at large L for different parameter values.

We propose a series of paired spin-singlet quantum Hall states, which exhibit a separation of spin and charge degrees of freedom. The fundamental excitations over these states, which have filling fraction ν = 2 2m+1 with m an odd integer, are spinons (spin-1 2 and charge zero) or fractional holons (charge ± 1 2m+1 and spin zero). The braid statistics of these excitations are non-abelian. The mechanism for the separation of spin and charge in these states is topological: spin and charge excitations are liberated by binding to a vortex in a p-wave pairing condensate. We briefly discuss related, abelian spin-singlet states and possible transitions.

We present results for the ground states of a system of spin-1 bosons in a rotating trap. We focus on the dilute, weakly interacting regime, and restrict the bosons to the quantum states in the lowest Landau level (LLL) in the plane (disc), sphere or torus geometries. We map out parts of the zero temperature phase diagram, using both exact quantum ground states and LLL mean field configurations. For the case of a spin-independent interaction we present exact quantum ground states at angular momentum L ≤ N . For general values of the interaction parameters, we present mean field studies of general ground states at slow rotation and of lattices of vortices and skyrmions at higher rotation rates. Finally, we discuss quantum Hall liquid states at ultra-high rotation.