Quantum Hall States and Boson Triplet Condensate for Rotating Spin-1 Bosons

We propose and analyze two series of clustered quantum Hall states for rotating systems of spin-1 bosons. The first series [labeled $\mathrm{S}\mathrm{U}(4{)}_k$] 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 $\mathrm{S}\mathrm{O}(5{)}_k$, includes exact ground states at large $L$ for different parameter values.