Effective Hamiltonian for HTSC cuprates taking into account electron-phonon interaction in the strong-correlation regime

Electron-phonon interaction is sequentially derived from a realistic p-d multiband model for the cuprates under conditions of strong electron correlations. The electronic structure is described using the representation of the Hubbard X operators in a generalized tight-binding method. Dependences of the diagonal and off-diagonal (on lattice sites) matrix elements of electron-phonon interaction on the wavevectors are found for three phonon modes, namely, breathing, apical breathing, and bending modes. The interactions of the breathing and bending modes with electrons are shown to contribute to the formation of kinks in the (0; 0)-(π; π) and (0; 0)-(π; 0) directions, respectively. A low-energy t-J* model with phonons is developed; apart from electron-phonon interaction, it also includes spin-phonon interaction. The elimination of phonons gives an effective electron-electron interaction that depends on the occupation number of a multielectron term and on the carrier concentration due to strong electron correlations.