VALIDITY OF THE T-J MODEL - QUANTUM NUMBERS FOR (CU4O8)-7

Starting from the three-band Hubbard Hamiltonian, we eliminate the states containing Cu+ and Cu+3 by means of a standard canonical transformation. We diagonalize the resulting effective Hamiltonian for a Cu4O8 cluster with periodic boundary conditions, for zero and one added holes. Each eigenstate is classified according to the total spin, z projection and symmetry properties under operations of the complete symmetry group (which is larger than the space group). We repeat this procedure for the t - J model. t and J are obtained minimizing the mean square deviation-sigma between the lowest, energies of both models for each set of quantum numbers. For one added hole, sigma turns out to be larger or of the order of t, even in those cases in which the mapping was claimed to be exact. The t - J model cannot quantitatively reproduce band dispersion or symmetry properties of the eigenstates of lowest energy of doped CuO2 planes.