Ground state of the two-dimensional antiferromagnetic Heisenberg model and the resonating-valence-bond states

We have studied the relation between the resonating-valence-bond (RVB) state and the exact ground state for the two-dimensional antiferromagnetic (AF) Heisenberg model on a few small lattices. We describe a method to obtain the state of minimum energy within a family of RVB states. Based on the insight provided by the RVB states, and supported by our numerical results, we argue in favor of the existence of long-range order at T=0 for the two-dimensional AF Heisenberg model.