Effective Hamiltonian for cuprate superconductors

We compare numerical results of O and Cu occupations and optical and magnetic excitations for the three-band Hubbard model in a Cu4O8 cluster, with those obtained with an effective Hamiltonian Heff in which the Cu-O hopping tpd is eliminated by means of a canonical transformation. This transformation up to order tpd4 is not quantitatively valid when the relevant energy differences are of the order of √8 tpd or less. However, an Heff with the form of the second-order one, but which retains all higher-order terms contained in a CuO4 (Cu2O7) cluster for zero or one added hole (one added electron) to the undoped system, leads to a very good agreement with the results using the full Hilbert space. This Heff makes possible the numerical study of the three-band Hubbard model for realistic parameters, using larger clusters