Quantum Symmetry of Hubbard Model Unraveled

Superconducting quantum symmetries in extended single-band 1-dimensional Hubbard models are shown to originate from the classical (pseudo-)spin SO(4) symmetry of a class of models of which the standard Hubbard model is a special case. Extending the notion of symmetry to include quantum groups allows us to introduce extra parameters but the corresponding quantum symmetric models are restricted to one dimension. All models discussed are related by generalized Lang-Firsov transformations, some have symmetries away from half filling. The most general model with symmetric next-neighbour interaction terms and classical SO(4) symmetry is given explicitly.