Three-band Hubbard model: A Monte Carlo study

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∼t/30, where t is the Cu-O hybridization. For generally accepted values of the Hubbard coupling on the Cu sites ${\mathit{U}}_{\mathit{d}}$≳6t, two different regimes can be distinguished in the magnetic properties of the model. In the half-filled band case we see for Δ>${\mathit{U}}_{\mathit{d}}$/2 (Δ=${\mathrm{\varepsilon }}_{\mathit{p}}$-${\mathrm{\varepsilon }}_{\mathit{d}}$ being the charge-transfer energy) the formation of a correlation gap, as expected for a charge-transfer insulator. For Δ<${\mathit{U}}_{\mathit{d}}$/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 (δ≲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 δ≃0.2. Finally, we find evidence for an attractive pairing interaction only in the extended s-wave channel for δ=0.2 and β≳4/t, although no phase transition to a superconducting state could be seen.