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Numerical studies on Mott transitions caused by the control of the ratiobetween bandwidth and electron-electron interaction ($U$) are reported. Byusing the recently proposed path-integral renormalization group(PIRG)algorithm, physical properties near the transitions in the ground state oftwo-dimensional half-filled models with the nearest and the next-nearestneighbor transfers ($-t$ and $t'$, respectively) are studied as a prototype ofgeometrically frustrated system. The nature of the bandwidth-controltransitions shows sharp contrast with that of the filling-control transitions:First, the metal-insulator and magnetic transitions are separated each otherand the metal-insulator (MI) transition occurs at smaller $U$, although theboth transition interactions $U$ increase with increasing $t'$. Bothtransitions do not contradict the first-order transitions for smaller $t'/t$while the MI transitions become continuous type accompanied by emergence of{\it unusual metallic phase} near the transition for large $t'/t$. Anonmagnetic insulator phase is stabilized between MI and AF transitions. Theregion of the nonmagnetic insulator becomes wider with increasing $t'/t$. Thephase diagram naturally connects two qualitatively different limits, namely theHartree-Fock results at small $t'/t$ and speculations in the strong couplingHeisenberg limit.Comment: 30 pages including 20 figure

Magnetic and Metal–Insulator Transitions through Bandwidth Control in Two-Dimensional Hubbard Models with Nearest and Next-Nearest Neighbor Transfers