Dynamical mean field theory of correlated electron systems: New algorithms and applications to local observables

We perform a numerical study of local observables in correlated electron systems, with a particular emphasis on optical properties at interactions in the vicinity of the Mott transition region. Our calculations rely on solving the Dynamical Mean-Field equations corresponding to a single-band Hubbard Hamiltonian.;We begin by introducing the theoretical framework and presenting the general features of the Hubbard model and the Dynamical Mean-Field Theory. We discuss the approximations involved and the advantages gained in the ability to qualitatively understand the physics of correlated electron systems.;We continue with a description of the algorithms used in our calculations. We discuss the classic Hirsch-Fye impurity solver and its domain of aplicability. We describe the modifications that we introduced in order to overcome some of its limitations. We also present a new, continuous time impurity solver that enables a precise study of the single-band Hubbard model over a much wider range of temperature and interaction values.;Next we discuss the application of the numerical algorithms to Dynamical Mean-Field calculations. We begin with a study of the antiferromagnetic phase and present the successes and challenges of our applied methods. We then focus on the kinetic energy properties of the paramagnetic Hubbard model away from half-filling and perform a systematic analysis of its dependence on doping, temperature and interaction strength.;We conclude with a quantitative study of optical properties of the high- Tc cuprate compounds in the normal state. We parametrize the doping dependent transfer of spectral weight observed in experimental measurements and compare it with calculations performed for the single-band Hubbard model. Based on a systematic analysis of the interaction effects in the numerical results we put forth an argument for the correlation strength in high-Tc cuprates.