Wannier Representation for the Three-Band Hubbard Model

We obtain the cell representation for the Hamiltonian of the $(d-p)$ model. We use the Wannier orbitals for the holes belonging to the copper and oxygen ions; the orbitals are orthogonalized on the sites of the copper lattice. The first stage of calculating is diagonalizing the kinetic energy of the oxygen holes and, on this basis, introducing two diagonalizing orbitals for the oxygen fermions. These last two modes have significantly different local energies, which noticeably affect the results in the theory. The obtained Hamiltonian is represented as the sum of a main local term and a perturbation defining the delocalization of the Wannier fermions. We find the low-lying states and the corresponding energy spectrum for the local Hamiltonian. We show that introducing the diagonalizing fermions causes a significant lowering of the energy of the Zhang–Rice singlet.