Two-band singlet-hole model for the copper oxide plane

An effective Hubbard model for one-hole d-like states and two-hole singlet states is derived from the original p-d model to describe the low-energy electronic spectrum of the ${\mathrm{CuO}}_2$ plane in cuprates. By using the projection technique for the two-time matrix Green’s function in terms of Hubbard operators a two-band spectrum for d-like holes and singlets as well as the density of states is calculated. It is found that the hybridization between d-like holes and singlets results in a substantial renormalization of the spectrum. In addition, the dispersion relation depends strongly on the antiferromagnetic short-range spin correlations in the spin-singlet state: For large spin correlations at small doping values one finds a next-nearest-neighbor dispersion. With doping, by decreasing the spin correlations, the dispersion changes to an ordinary nearest-neighbor one.