The
CuO2 sheets common to the superconducting cuprates are believed to be characterized by a charge-transfer gap in their insulating antiferromagnetic state. The three-band Hubbard model with an on-site Cu Coulomb interaction
Ud, which is large compared to the difference in energy \ensuremath{\varepsilon} between the O and Cu sites, provides a basic model for such a system. We have carried out Lanczos and Monte Carlo studies of a
CuO2 lattice described by a three-band Hubbard model. For
Ud large compared with \ensuremath{\varepsilon}, and \ensuremath{\varepsilon} comparable to or larger than the bandwidth of the lower hole band, we find strong antiferromagnetic correlations and evidence for a charge-transfer gap at a filling of one hole per Cu. The antiferromagnetic correlations decrease with either hole or electron doping, and we see that the additional holes go primarily on the O sites, while additional electrons go onto the Cu sites. For large values of the intersite Cu-O Coulomb interaction V, the hole-doped system exhibits a charge-transfer instability. As V is reduced, this is reflected as a peak in the charge-transfer susceptibility near \ensuremath{\varepsilon}+2V\ensuremath{\approxeq}
Ud, which we find is washed out by the strong Cu-O hybridization at realistic values of V. Attractive pairing interactions are found in both the d-wave and extended
s∗-wave channels near the antiferromagnetic boundary.
We present in this article results of Quantum Monte Carlo simulations for the three-band Hubbard model obtained both with the grand canonical approach as well as with the T =0 formalism. A direct comparison of Quantum Monte Carlo results with experimental values for the charge-transfer gap leads to a set of parameters for the three-band Hubbard model that consistently describes salient features of the high- T c superconductors. We find long-range antiferromagnetic order in the undoped case as well as an incommensurate structure for a doping concentration of δ≈0.20. Moreover the magnetic susceptibility as a function of doping δ is in a qualitative agreement with experiments. Concerning dynamical properties, we have evaluated the spectral density [Formula: see text]. The dispersion of the state with the lowest excitation energy is in very good agreement with experimental photoemission and inverse photoemission experiments for a doping concentration of δ=0.25. In the superconducting regime, we find that the interaction vertex for the pairing correlation function in the extended s-channel shows a maximum for δ~0.20, resembling the dependence of T c on doping. This feature is not present for other symmetries of the order parameter or in other parameter regions.