Three-band Hubbard model: A Monte Carlo study.

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We have studied a two-dimensional multiband Hubbard model describing ${\mathrm{CuO}}_{2}$ sheets in the high-${\mathit{T}}_{\mathit{c}}$ oxides. The simulations were performed for a grand-canonical ensemble on lattice sizes up to 16 unit cells of three atoms each and temperatures down to ${\mathit{k}}_{\mathit{B}}$T\ensuremath{\sim}t/30, where t is the Cu-O hybridization. For generally accepted values of the Hubbard coupling on the Cu sites ${\mathit{U}}_{\mathit{d}}$\ensuremath{\gtrsim}6t, two different regimes can be distinguished in the magnetic properties of the model. In the half-filled band case we see for \ensuremath{\Delta}g${\mathit{U}}_{\mathit{d}}$/2 (\ensuremath{\Delta}=${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{p}}$-${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{d}}$ being the charge-transfer energy) the formation of a correlation gap, as expected for a charge-transfer insulator. For \ensuremath{\Delta}${\mathit{U}}_{\mathit{d}}$/2, on the other hand, no gap is visible in the considered temperature region. In this (mixed-valence) situation only a very weak dependence of the magnetic structure form factor on doping is obtained, in contrast to the charge-transfer situation, where a strong decrease of the same quantity is observed for very low concentrations of dopant holes (\ensuremath{\delta}\ensuremath{\lesssim}0.05). The existence of antiferromagnetic long-range order in the two different parameter regions is studied with finite-size scaling in the low-temperature regime. We also investigated the possibility of singlet formation between O holes and the Cu hole on one plaquette, as suggested by Zhang and Rice. The amplitude squared of such a singlet increases strongly as a function of doping, reaching saturation at \ensuremath{\delta}\ensuremath{\simeq}0.2. Finally, we find evidence for an attractive pairing interaction only in the extended s-wave channel for \ensuremath{\delta}=0.2 and \ensuremath{\beta}\ensuremath{\gtrsim}4/t, although no phase transition to a superconducting state could be seen.