Spin-1 liquid on pyrochlore and checkerboard lattices

We construct a local SU(2) symmetric spin-1 Hamiltonian on the 3D pyrochlore and 2D checkerboard lattices. The ground states of the Hamiltonian are known exactly; they form an exponentially large degenerate manifold. These ground states are characterised by an exponential decay of spin-spin correlations, which strongly suggests a spin gap. By perturbing the Hamiltonian with additional Heisenberg terms we can lift the ground state degeneracy and analyse the nature of the singlet sector of the Hilbert space. We also discuss the possibility of fractionalised edge/surface states.