Critical properties of metal-insulator transition in low dimensions

Anomalous metallic states near the Mott insulator are analyzed in terms of the critical scaling toward the metal-insulator transition. Continuous transitions from a metal to the Mott insulator are characterized either by the mass divergence as in the bi-component systems or the vanishing carrier number as in the valence bond systems. A set of critical exponents in these two cases is deduced from the scaling theory. The correlation exponent v and the dynamical exponent z satisfy v = 1/2 d and z = 2 d when the mass diverges in d dimensions, while v = 1/2 and z = 2 if the carrier number vanishes. Crossovers between quantum critical regime and thermal critical regime inferred from this theory shed light on understanding experimental indications in high-T_c cuprates and other strongly correlated systems.