Symmetries of 1D Hubbard model with variable range exchange

Abstract:
Two pairs of Y(sl₂) Yangian symmetries for the trigonometric and hyperbolic versions of the 1D Hubbard model with variable range hopping are presented. In both cases the Yangians are mutually commuting, hence can be combined into a Y(sl₂)ÅY(sl₂) Yangian. The examples of scalar integrals of motion are also obtained for most general model with elliptic hopping. These findings provide clear indication to the complete integrability of the above models.