Exact ground and excited states of frustrated antiferromagnets on the CaV4O9 lattice

The experimental observation of a spin gap in the antiferromagnetic spin-1/2 compound CaV4O9 has been attributed to the formation of a plaquette-resonating-valence-bond (PRVB) state in the underlying 1/5-depleted square lattice. We construct a spin-1/2 model on the 1/5-depleted lattice for which the PRVB state can be shown to be the exact ground state in a particular parameter regime. In a subspace of this parameter regime, the first excited state can be calculated exactly. In a different parameter regime, the dimer state is shown to be the exact ground state.