VALIDITY OF THE T-J MODEL

We have diagonalized exactly an effective Hamiltonian H(eff) that describes the low-energy eigenstates of a Cu4O8 cluster with five holes. Projecting these eigenstates onto Zhang-Rice states we find that for total spin S=1/2, they have more than 90% of local singlet character for realistic parameters. This percentage depends on S and the symmetry of the states and is larger for the ground state. The fit of the energy levels using a model similar to the t-J model, is improved substantially if the model includes a term that combines a nearest-neighbor exchange with a next-nearest-neighbor hopping.