Peculiarities of pair interaction in the four-band Hubbard model

We consider the four-band model of high-temperature superconductors with copper {\rm3d}$_{x^2-y^2}$ and {\rm4s} electrons and oxygen {\rm2p}$_x$ and {\rm2p}$_y$ electrons. We assume that the Coulomb repulsion between the copper {\rm3d} electrons is strong. We diagonalize the oxygen subsystem and pass to the Wannier representation for the CuO$_2$ cluster. We study the properties of a local cell model and find its low-energy states such as the one-particle doublet and the two-particle singlet and triplet states. We consider the cell fermion delocalization because of their tunneling between the copper sites. We obtain a system of Dyson-type equations for renormalized one-particle Green's functions and discuss whether it can be simplified.