Single-, triple-, or multiple-band Hubbard models

The relevance of different models, such as the one-band t-J model and the three-band Emery model, as a realistic description of the electronic structure of high-${\mathit{T}}_{\mathit{c}}$ materials is discussed. Starting from a multiband approach using cluster calculations and an impurity approach, the following questions are addressed: What is the stabilization energy of the Zhang-Rice singlet and triplet with respect to other symmetry levels (such as the ${\mathit{d}}_{3\mathit{z}}^2$-${\mathit{r}}^2$, etc.)? How does the oxygen 2p-band width (${\mathit{t}}_{\mathit{p}\mathit{p}}$) influence the stability of the Zhang-Rice singlet? How large is the dispersion of the singlet state? It is argued that, if the one-band model does not give a satisfactory description of the low-energy physics, then the three-band model will be incomplete as well.