We study electronic phase transitions in the half-filled ionic Hubbard model with an on-site Coulomb repulsion U and an ionic energy Δ by using the coherent potential approximation. For a fixed and finite Δ two transitions from the band insulator via a metallic state to a Mott insulator are found with increasing U. The values of the critical correlation-driven metal-insulator transitions U(c1)(Δ) and U(c2)(Δ) are estimated. Our results are in reasonable agreement with the ones obtained by single-site dynamical mean-field theory and determinant quantum Monte Carlo simulation.

We study charge ordering (CO) in the extended Hubbard model with both on-site and nearest-neighbour Coulomb repulsion (U and V , respectively) within the coherent potential approximation. The phase boundary between the homogeneous and charge-ordered phases for the square lattice is obtained for different values of U . It is shown that at quarter-filling for all values of U the CO exists only if the inter-site Coulomb repulsion V exceeds certain a critical value which is of the order of the kinetic energy t. At finite temperature a re-entrant transition is found in some region of V .

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