Strongly correlated electrons studied by numerical and scaling approaches

I review recent progress in understanding metal-insulator transitions of strongly correlated electron systems. In particular, using improved algorithms of quantum Monte Carlo calculations, the universality class of the transition between the Mott insulator and metals in two dimensions has been clarified and analyzed numerically and compared with the prediction from the scaling theory. It shows the existence of new universality class of the metal-insulator transition characterized by unusual suppression of coherence in the metallic side due to a large dynamical exponent. Its relevance to understand the unusual metallic states near the Mott insulator widely observed in transition metal compounds such as high-Tc cuprates and manganites is discussed.