Local fluctuations in the metal-insulator transition

We studied some aspects of the two-dimensional metal-insulator transition in the disordered case using the Hubbard model through the Statistical Dynamical Mean-Field Theory. We obtained the spinodal lines at which metal and insulator cease to be meta-stable. We also studied the spatial fluctuations of local quantities, such as the self-energy and the local Green's function for different disorders and temperature values. We showed the appearance of metallic "bubbles" within the insulator and vice-versa. We performed an analysis of finite-size effects and showed that the first-order transition is smeared in the thermodynamic limit. We analyzed transport properties by mapping to a random classical resistor network and calculating both the average current and its distribution across the Mott metal-insulator transition. We studied the domain wall's behavior, which forms between the metal and the insulator in the clean case, by employing a one-dimensional chain model connected to two reservoirs, one metallic at the left side and another insulating at the right side, each attached to one of the chain's ends. We then obtained the domain wall width as a function of temperature and interactions.