Single-band Hubbard model with spin-orbit coupling

A single-band Hubbard hamiltonian with spin-orbit coupling included in the hopping integral is solved in terms of the solution with no spin-orbit coupling. For an openended linear chain the spectrum is independent ofu/t=tan θ, whereu(t) measures the spin-orbit (ordinary) contribution to the hopping integral; and for the half-filled band the spin-correlations are spiral-like with turn angle 2θ+π. In the case of a ring ofN sites the spectrum is periodic in θ with period 2π/N; for the half-filled-band case the period is π/N in the zero-band-width limit. Generalizations to higher dimensions are noted.