Spin-charge separation in the 1D Hubbard model with longer-range hopping

Although it is very hard to solve the 2D Hubbard model in the U --> infinity limit, progress can be made using a class of 1D models in which additional longer range-hopping is included. Here, an unusual form of mean field theory is used to study the charge motion in the simplest model of the class - that with nearest and next next nearest neighbour hopping. The solutions found are all spin-charge separated, and for lower electron densities, indications of hard core boson like behaviour for the charge degrees of freedom are seen. For higher electron densities Nagaoka ferromagnetism is seen.