We perform a thorough study of the extended Hubbard model featuring local and nearest-neighbor Coulomb repulsion. Using the dynamical mean-field theory we investigated the zero-temperature phase diagram of this model as a function of the chemical doping. The interplay between local and nonlocal interactions drives a variety of phase transitions connecting two distinct charge-ordered insulators, i.e., half filled and quarter filled, a charge-ordered metal and a Mott-insulating phase. We characterize these transitions and the relative stability of the solutions and we show that the two interactions conspire to stabilize the quarter-filled charge-ordered phase.
We consider two aspects of the ground state of the $U=\ensuremath{\infty}$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\ensuremath{\infty}$ Hubbard ladder in the limit of the large interchain hopping ${(t}_{\ensuremath{\perp}}/t\ensuremath{\rightarrow}\ensuremath{\infty})$. In this limit, the total spin
S of the ground state is shown to be zero for the electron density
n< 0.5 and its maximum
(S=Smax) for
n>0.5. The charge gap at quarter-filling is ${2t}_{\ensuremath{\perp}}.$ We extend these results to finite ${t}_{\ensuremath{\perp}}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite ${t}_{\ensuremath{\perp}}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio ${t}_{\ensuremath{\perp}}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the
t-
J ladder is briefly discussed.