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We calculate the temperature dependent conductivity in the half-filled ionic Hubbard model with an on-site Coulomb repulsion $U$ and an ionic energy $\Delta$ by mean of the coherent potential approximation. It is shown that for intermediate and large \(\Delta\) the largest conductivity occurs near the special value \(U = 2 \Delta\) at all temperatures \(T\), for a fixed \(\Delta\) the region of finite conductivity \([U_{c1}, U_{c2}]\) expands and its maximum decreases with increasing \(T\). Our results are in good agreement with those derived from the determinant quantum Monte Carlo simulation.

The Mott - Hubbard metal - insulator transition in the half-filled mass imbalanced ionic Hubbard model is investigated using the two-site dynamical mean field theory. We find that for a fixed mass imbalanced parameter r the critical interaction Uc increases when the ionic energy \(\Delta\) is increased. In the other hand, for a fixed \(\Delta\), \(U_c\) decreases with increasing the mass imbalance. We also show the existence of BI phase in the system for the case \(\Delta \ne 0\), \(U=0\) and calculate the staggered charge density \(n_B − n_A\) as a function of the interaction for different values of the mass imbalance. Our results in the limiting cases (\(r = 1\); \(\Delta \ne 0\) or/and \(\Delta = 0\); \(r\ne 1\)) are in good agreement with those obtained from full dynamical mean field theory.

The electronic phase diagram of strongly correlated systems with disorder is constructed using the typical-medium theory. For half-filled system, the combination of the linearized dynamical mean field theory and equation of motion approach allows to derive the explicit equations determining the boundary between the correlated metal, Mott insulator, and Anderson insulator phases. Our phase diagram is consistent with those obtained by the more sophisticated methods.

We study a two-band Hubbard model using the Coherent Potential Approximation (CPA) and equation of motion decoupling scheme with scattering correction (Hubbard-III-I approximation). We show that above two approximations are completely equivalent to each other for the Periodic Anderson Model (PAM) as well as for the Self-doped Mott System (SMS).

Using coherent potential approximation we study zero-temperature Mott transition of the half-filled Hubbard model in a two-dimensional square lattice with geometrical frustration. It turns out that the geometrical frustration reduces the gap between the Hubbard bands. As a result the metallic phase is stabilized up to a fairly large value of the on-site Coulomb interaction. We found that the critical value UC for the Mott transition is enhanced by the geometrical frustration. Our results are in good agreement with the ones obtained by the single-site dynamical mean-field theory. Mott-insulator; Hubbard model; geometrical frustration; coherent potential approx- imation.

The electronic properties of strongly correlated systems with binary type of disorder are investigated using the coherent potential approximation. For half-filled system, two transitions from a band insulator via a metallic state to a Mott insulator are found with increasing the correlation strength of only one of the constituents. Our phase diagram is consistent with those obtained by the dynamical mean field theory.

The half-filled isotropic degenerate two-band Hubbard model is studied within coherent potential approximation. The model is characterized by an Ising-type Hunds exchange coupling, intraand inter-orbital Coulomb parameters. We found that the band degeneracy slightly reduces the Mott-Hubbard critical value UC . We reveal that the system can have two distinct critical values for Mott-Hubbard transitions.

We investigate the influence of an unoccupied band on the transport properties of a strongly correlated electron system. For that purpose, additional orbitals are coupled to a Hubbard model via hybridization. The filling is one electron per site. Depending on the position of the additional band, both, a metal--to--insulator and an insulator--to--metal transition occur with increasing hybridization. The latter transition from a Mott insulator into a metal via ``self--doping'' was recently proposed to explain the low carrier concentration in $\rm Yb_4As_3$. We suggest a restrictive parameter regime for this transition making use of exact results in various limits. The predicted absence of the self--doping transition for nested Fermi surfaces is confirmed by means of an unrestricted Hartree--Fock approximation and an exact diagonalization study in one dimension. In the general case metal--insulator phase diagrams are obtained within the slave--boson mean--field and the alloy--analog approximation., 9 pages, Revtex, 6 postscript figures

The Hubbard model of strongly correlated electron systems is considered near half-filling within the framework of a new functional integral method without slave bosons. A dynamical system of equations determining the superconducting phase of the Hubbard model is derived. Both singlet and triplet Cooper pairings are studied.