| The aim of this dissertation is to develop a methodology based on a dynamical mean-field theory to study quantum fluctuations in a strongly correlated electron system in which correlations are relatively short-ranged, and to analyze real examples of quantum phase transition for which application of this method is valid.; A dynamical mean-field theory maps a lattice problem to an effective local problem supplemented by a time-dependent self-consistent field in which quantum fluctuations are retained via a time-dependence of self-consistent field, and thus provides a rigorous approach to study quantum many-body phenomena to the extent the above mapping is valid. It is argued that this mapping is justified when the physics under consideration originates in sufficiently short-range correlations of relevant degrees of freedom.; In Part I, Mott Transition in the presence of a long-range antiferromagnetic order is studied based on the two-band Hubbard Model. In the effective impurity picture, Mott transition is interpreted as onset of local gapless single-particle excitation and is signaled as a Kondo-like resonance in the single-particle spectra. It is argued that in the effective impurity model of the two-band Hubbard model, Kondo screening and RKKY interaction do not necessarily represent the same energy scale and this can lead to the afore-said transition. Numerical results are consistent with the above arguments. The results are also consistent with the experimental observation of NiS2−xSex.; In Part II, Superconductivity in a doped Mott insulator is studied based on the self-consistent two-site cluster model mapped from the one-band Hubbard model. This approach is essentially an extension of BCS theory in which non-local but short-range quantum fluctuations are rigorously treated. The overall results provide a consistent interpretation of the experiments on high-Tc cuprates. In particular, a strong connection between antiferromagnetic spin fluctuations and pairing correlations is revealed, and a calcutated staggered spin susceptibility develops a resonnance-like sharp peak in a superconducting phase. |
