A soluble model for a Spin-1 Kagom\'{e} Antiferromagnet

We propose an exactly soluble spin-1 model on a $2D$ Kagom\'{e} lattice. The Klein-type Hamiltonian involves interactions between nearest and next-nearest spins and, unlike the closely related AKLT Hamiltonians, has extensively degenerate ground states. These ground sates are characterised by an exponential fall-off of correlations between spins which strongly suggests a gap to the excited states. Simple spin-1 and spin-0 excitations can be viewed as bound states of $S=1/2$ spinons. We also show that generic Heisenberg-like perturbations lead to a unique ground state -- a featureless fluctuating valence bond ``solid'' obtained by placing a benzol ring on every hexagon of the lattice. Finally, we consider an additional term of the type $\alpha ({S^z})^2$ which can drive the system into another featureless ground state. We introduce the notion of ``wedge'' excitations that allow to distinguish between these states leading to the conclusion that these sates must be separated by at least one quantum phase transition.