| In this thesis we study the strongly correlated electron physics in the framework of the longstanding H-TC superconductivity problem using a non-perturbative method, the Dynamical Mean Field Theory (DMFT), capable to go beyond standard perturbation theory techniques. DMFT is by construction a local theory which neglects spatial correlation. The latter is however shown in experiments to be a fundamental property of cuprate materials. In a first step, we approach the problem of the spatial correlation in the normal state of cuprate materials using a phenomenological Fermi-Liquid-Boltzmann model. We then introduce and develop in detail an extension to DMFT, the Cellular Dynamical Mean Field Theory (CDMFT), capable of considering short-ranged spatial correlation in a system and implemented it with the exact diagonalization algorithm. After testing CDMFT in an exact limiting case, we apply it to study the density-driven Mott metal-insulator transition in the two-dimensional Hubbard Model with particular attention to the anomalous properties of the normal state as the Mott insulator is approached. We finally study the superconducting state. We show that within CDMFT the one-band Hubbard Model supports a d-wave superconductive state, which strongly departs from the standard BCS theory. We conjecture a link between the instabilities found in the normal state and the onset of superconductivity. |
