The derivation and the physical properties of the ‘t-J +3-sites hopping’ model

We derive the effective Hamiltonian for high T c cuprates by perturbation theory and cluster calculation. The obtained Hamiltonian is the ‘t-J+3-site hopping’ model, which consists of the hopping, superechange and spin dependent 3-sites hopping terms. The last term is ferromagnetic for the hole doped systems, in contrast to that derived from the single band Hubbard model. The physical properties of the model is investigated by the slave boson mean field theory. It turns out that the ferromagnetic 3-sites hopping term enhances considerably the singlet RVB order.