Density functional theory along with Kohn-Sham formalism (DFT-KS) works well for weakly correlated electron systems such as alkali metals or systems involving atoms belonging to the first or second row of the periodic table. As a result, DFT-KS and its variants such as local spin density approximation (LSDA) or the generalized gradient approximation (GGA) encounter difficulties when applied to strongly correlated electron systems (SCES), such as transition metals, high-T_c superconductors (HTCS) and heavy fermion systems.

     Gutzwiller and Hubbard separately worked on "effect of correlation on the ferromagnetism of transition metals" and introduced the well-known Hubbard model (HM). It is believed that HM has the basic ingredients to describe the Mott transitions, magnetic transitions, as well as the properties of HTCS.

     Lieb and Wu, by employing the Bethe-ansatz, have been able to obtain exact analytical solution of the one-dimensional Hubbard model (1DHM). We have studied their work and tried to develop a similar scheme for 2DHM suitable for HTCS. However, since at the present time, exact solutions of 2DHM are not available, we have also reviewed the dynamical mean field theory (DMFT) and the numerical methods for solving the equations in this scheme. In this theory an effective imaginary time action is defined in terms of the bare Green’s function g₀(τ- τ’). g₀(τ- τ’) plays the role of time dependent mean field. The computer code for DMFT is reproduced. Since, at this stage, through the mapping of the infinite dimensional HM onto Anderson impurity model (AIM), the spatial fluctuations of the self-energy are ignored, we have also considered quantum cluster method and produced its computer code. Our aim is to use a generalized form of the HM, employ the necessary modification in our computer codes, and investigate the properties of HTCS cuprates.

     In the mean time, we have studied the various numerical techniques such as quantum Monte Carlo method, the exact diagonalization technique and the non-crossing approximation for our numerical purposes.

     Finally, we are studying the symmetries of the generalized HM, and their relation to s and d wave superconductivity as well as charge density waves (CDW).

     Our group consisting of N. Nafari, R. Asgari and R. Noorafkan has been studying the Hubbard model and its application to HTCS.