The paper continues the rigorous investigations of the mean field Green function solution of the effective two-dimensional two-band Hubbard model [N. M. Plakida et al., Phys. Rev. B, Vol.51, 16599 (1995)] of the superconducting phase transitions in c
uprates, started in [Gh. Adam, S. Adam, J. Phys. A: Math. Theor., Vol.40, 11205 (2007)]. Discussion of the $(delta, T)$ phase diagram of the model points to the divergence of the energy spectrum in the limit of vanishing doping $delta$. Finite energy spectra at all possible doping rates $delta$ are obtained provided the hopping part of the effective Hamiltonian is renormalized with an effective factor pointing to the site-pairs availability for fermion hopping processes.
The Green function (GF) equation of motion technique for solving the effective two-band Hubbard model of high-T_c superconductivity in cuprates [N.M. Plakida et al., Phys. Rev. B, v. 51, 16599 (1995); JETP, v. 97, 331 (2003)] rests on the Hubbard ope
rator (HO) algebra. We show that, if we take into account the invariance to translations and spin reversal, the HO algebra results in invariance properties of several specific correlation functions. The use of these properties allows rigorous derivation and simplification of the expressions of the frequency matrix (FM) and of the generalized mean field approximation (GMFA) Green functions (GFs) of the model. For the normal singlet hopping and anomalous exchange pairing correlation functions which enter the FM and GMFA-GFs, an approximation procedure based on the identification and elimination of exponentially small quantities is described. It secures the reduction of the correlation order to GMFA-GF expressions.
