FERROMAGNETIC TRANSITION AND PHASE-DIAGRAM OF THE ONE-DIMENSIONAL HUBBARD-MODEL WITH NEXT-NEAREST-NEIGHBOR HOPPING

We study the phase diagram of the one-dimensional Hubbard model with n ext-nearest-neighbor hopping using exact diagonalization, the density- matrix renormalization group, the Edwards variational ansatz, and an a daptation of weak-coupling calculations on the two-chain Hubbard model . We find that a substantial region of the strong-coupling phase diagr am is ferromagnetic, and that three physically different limiting case s are connected in one ferromagnetic phase. At a point in the phase di agram at which there are two Fermi points at weak coupling, we study c arefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We pres ent evidence that the transition is second order and determine the cri tical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Lu ttinger-liquid parameters and show how their behavior differs from tha t of the nearest-neighbor Hubbard model. The general weak-coupling pha se diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validit y by numerically calculating spin and charge gaps using the density-ma trix renormalization group. [S0163-1829(98)08229-0].