Two-dimensional Disordered Mott Metal-Insulator Transition

We studied several aspects of the Mott metal-insulator transition in thedisordered case. The model on which we based our analysis is the disorderedHubbard model, which is the simplest model capable of capturing the Mottmetal-insulator transition. We investigated this model through the StatisticalDynamical Mean-Field Theory (statDMFT). This theory is a natural extension ofthe Dynamical Mean-Field Theory (DMFT), which has been used with relativesuccess in the last several years with the purpose of describing the Motttransition in the clean case. As is the case for the latter theory, thestatDMFT incorporates the electronic correlation effects only in their localmanifestations. Disorder, on the other hand, is treated in such a way as toincorporate Anderson localization effects. With this technique, we analyzed thedisordered two-dimensional Mott transition, using Quantum Monte Carlo to solvethe associated single-impurity problems. We found spinodal lines at which themetal and insulator cease to be meta-stable. We also studied spatialfluctuations of local quantities, such as the self-energy and the local Green'sfunction, and showed the appearance of metallic regions within the insulatorand vice-versa. We carried out an analysis of finite-size effects and showedthat, in agreement with the theorems of Imry and Ma, the first-order transitionis smeared in the thermodynamic limit. We analyzed transport properties bymeans of a mapping to a random classical resistor network and calculated boththe average current and its distribution across the metal-insulator transition.