EFFECTIVE ONE-BAND HAMILTONIAN FOR CUPRATE SUPERCONDUCTOR METAL-INSULATOR-TRANSITION

Starting from the three-band Hubbard hamiltonian H and projecting out of the Hilbert space a group of high-energy states, we obtain an effective one-band model H(eff). H(eff) has a form similar to the Hubbard model, but the hopping terms depend on occupation numbers. We give analytical, accurate enough expressions relating the parameters of H(eff) to those of H. Treating H(eff) in an approximation similar to Hubbard III the problem is reduced to an alloy with diagonal and off-diagonal disorder. Using the criterion of the closing of the gap in this effective alloy for the metal-insulator transition, we obtain a metal-insulator phase diagram for the undoped system as a function of the parameters of H. The system is insulating for realistic parameters.