The extrapolation of small-cluster exact-diagonalization calculations is used to examine ferromagnetism in the one-dimensional Hubbard model with a generalized type of hopping. It is found that the long-range hopping with power decaying hopping amplitudes ${(t}_{\mathrm{ij}}\sim q^{|i-j|})$ stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n. The critical value of the interaction strength $U_c\mathrm{}\left(q\right)\mathrm{}$ above which the ferromagnetic state becomes stable is calculated numerically and the ground-state phase diagram of the model (in the $U-q$ plane) is presented for physically the most interesting cases.

• Received 11 March 2002

DOI:https://doi.org/10.1103/PhysRevB.66.012404