Ferromagnetism in the one-dimensional Hubbard model with long-range electron hopping and long-range Coulomb interaction

\n\nWe present a simple, but very realistic, model for a stabilization band ferromagnetism in strongly correlated electron systems. The model is based on a generalized description of electron hopping and electron interactions on a lattice within the frame of the Hubbard Hamiltonian. Instead of the usual nearest-neighbour hopping and on-site Coulomb interaction we consider the long-range electron hopping and the long-range Coulomb interaction both with exponentially decaying amplitudes. It is shown that the simultaneous presence of both long-range mechanisms leads to the stabilization of the ferromagnetic ground state for a wide range of Coulomb interactions and electron concentrations. In particular, it is found that the long-range interaction plays a crucial role in the stabilization of the ferromagnetic state for electron concentrations $n \\leq 1$ , while the long-range hopping for n > 1. Thus, one of the possible explanations of the absence of ferromagnetism in the ordinary Hubbard model (with the nearest-neighbour hopping and the on-site Coulomb interaction) could be the oversimplified description of electron hopping and electron interactions on the lattice. This opens a new route towards the understanding of band ferromagnetism in strongly correlated electrons systems.\n