Attractive interactions from repulsive forces in a multiband Hubbard model

An extended multiband Hubbard model of the two-dimensional Cu${\mathrm{O}}_2$ planes of high-$T_c$ superconductors is examined by exact diagonalization of the Hamiltonian for small clusters with periodic boundary conditions. Holes are shown to bind in the limit of large Cu-site and nearest-neighbor Cu-O Coulomb repulsion. A simple explanation of the source of the binding energy is given in this strong-coupling limit. The more realistic case of relatively weak nearest-neighbor repulsion is also examined, and suggestive evidence is presented that the effective attraction will also exist in the thermodynamic limit for this case.