In this research we focus on the analysis of electronic properties of crystals, which can be approximated by an effective lattice model. In strong correlation limit, one can usually use the Hubbard model to simulate many body behaviours of the system. We investigate two dimensional lattice systems, for possible Mott transition between insulating and metallic phases. Among computer based methods that provide important information about these properties, cluster perturbation theory, which was proposed by David Senechal, is one of the best methods. In this theory a lattice is split into similar clusters of finite size, for which one can determine the exact Green function. Then by many body perturbative diagrams, one can extend the solution to the lattice problem. Once the lattice Green function is obtained, the electronic properties such as spectral function nad density of states of the system would be calculated. We use Lanczos algorithm to find the cluster Green function, for 1-site and 2-sites clusters and tried to overcome programming problems for 4-sites clusters.
