Metal-insulator transition of correlated systems and origin of unusual metal

Transitions between the Mott insulator and metals in clean systems are analyzed with the scaling theory in terms of quantum critical phenomena. In the case of generic transitions controlled by the filling, the scaling theory is established from analyses of the Drude weight and the compressibility based on hyperscaling. In the transition to the Mott insulator, a new universality class with the correlation length exponent v<1/2 and the dynamical exponent z<2 is derived, which is in contrast to the transition to the band insulator characterized by v=1/2 and z=2. The unusual exponents lead to various anomalous characters of metals near the Mott insulator such as strong suppression of the degeneracy temperature, and nonlinear dependence of the Drude weight on the doping concentration. Remarkable properties are also found in the specific heat, the compressibility and spin correlations. A mechanism of high temperature superconductivity is discussed in terms of the release from the suppressed coherence.