THE ONE-DIMENSIONAL HUBBARD-MODEL WITH 1ST-NEAREST-NEIGHBOR, 2ND-NEAREST-NEIGHBOR AND 3RD-NEAREST-NEIGHBOR HOPPING IN THE STRONG-COUPLING LIMIT

Using an extension of the Jordan-Wigner transformation, we solve the one-dimensional Hubbard model at U = infinity in the limit of dominant nearest-neighbour hopping combined with infinitesimal hopping over slightly longer ranges. We find several possible phases at zero temperature, including ferromagnetism, paramagnetism (with and without a spin gap), and even long-range antiferromagnetism with a particular limiting procedure. Our solutions are always spin-charge separated, and we give evidence that the charge degrees of freedom are best described by bosonic statistics.