Abstract
Abstract 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 Cu 4 O 8 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 σ between the lowest energies of both models for each set of quantum numbers. For one added hole, σ 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 CuO 2 planes.
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