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One central challenge in high-$T_c$ superconductivity (SC) is to derive adetailed understanding for the specific role of the $Cu$-$d_{x^2-y^2}$ and$O$-$p_{x,y}$ orbital degrees of freedom. In most theoretical studies aneffective one-band Hubbard (1BH) or t-J model has been used. Here, the physicsis that of doping into a Mott-insulator, whereas the actual high-$T_c$ cupratesare doped charge-transfer insulators. To shed light on the related question,where the material-dependent physics enters, we compare the competing magneticand superconducting phases in the ground state, the single- and two-particleexcitations and, in particular, the pairing interaction and its dynamics in thethree-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e.the variational cluster approach (VCA), we find which frequencies are relevantfor pairing in the two models as a function of interaction strength and doping:in the 3BH-models the interaction in the low- to optimal-doping regime isdominated by retarded pairing due to low-energy spin fluctuations withsurprisingly little influence of inter-band (p-d charge) fluctuations. On theother hand, in the 1BH-model, in addition a part comes from "high-energy"excited states (Hubbard band), which may be identified with a non-retardedcontribution. We find these differences between a charge-transfer and a Mottinsulator to be renormalized away for the ground-state phase diagram of the3BH- and 1BH-models, which are in close overall agreement, i.e. are"universal". On the other hand, we expect the differences - and thus, thematerial dependence to show up in the "non-universal" finite-T phase diagram($T_c$-values).

The 3-Band Hubbard-Model versus the 1-Band Model for the high-Tc Cuprates: Pairing Dynamics, Superconductivity and the Ground-State Phase Diagram