Effects of strong correlation and randomness in the vicinity of the Mott transition in the quasi-one-dimensional Hubbard model

We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number D-perpendicular to -> infinity in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping delta = 1-n (n, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range l(perpendicular to). We find that the delta-dependence of these quantities shows nonuniversal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it ij shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of Mott glass state for delta -> 0, provided that there exists a finite range interaction.