Phase diagram of the simplified Hubbard model with a generalized type of hopping in an external magnetic field

The extrapolation of small-cluster exact-diagonalization calculations is used to examine the zero-temperature phase diagram of the simplified Hubbard model in an external magnetic field. Using a general expression for hopping matrix elements (t(ij) similar to q(\i-j\)) the influence of the long-range hopping (the asymmetry of the density of states) on ground-state properties, and particularly on ferromagnetism is studied. It is found that the long-range hopping (the asymmetric density of states) stabilizes the ferromagnetic state for a wide range of electron interactions U and electron concentrations n. The critical value of magnetic field h below which the ferromagnetic state becomes unstable is calculated numerically. It is shown that below this critical value the ferromagnetic state breaks down into a metallic state for weak coupling and an insulating state for strong coupling. The phase diagram of the model in the h-U plane is presented for physically the most interesting cases.