Mott-hubbard Metal-insulator Transition and Optical Conductivity in High Dimensions

The main focus of this work are studies of correlated electron systems near a Mott metal-insulator transition. In particular, we will present the first controlled DMFT calculation of the complete phase diagram of the fully frustrated single-band Hubbard model with semi-elliptic density of states at half filling using the QMC method. We will also perform the first calculations of the associated optical conductivity which do not depend on the assumption of anisotropy or disorder; these will be based on the general theory of densities of states and transport properties in high dimensions which is also developed in this thesis. In addition to these pure model studies, we will present results specific to the doped transition metal oxide La1-xSrxTiO3 which are obtained using the hybrid LDA+DMFT technique. This new method employs ab initio density functional theory in the local density approximation (LDA) for defining a general multi-band Anderson-Hubbard model which is then treated within the DMFT.