Two-dimensional spin models with resonating valence bond ground states

Two spin models in two dimensions are constructed for which the exact ground states can be written down in a certain parameter regime of the Hamiltonian. The ground state of the first model is a local resonating valence bond (RVB) state in which not all the spins participate in resonance. The ground state is highly degenerate and there is a gap in the excitation spectrum. The second model is shown to have a ground state which is a quantum spin liquid with all the spins taking part in resonance. The ground state obtained is non-degenerate and there is no gap in the excitation spectrum.