Quantum symmetries induced by phonons in the Hubbard model

We show how the addition of a phonon field to the Hubbard model deforms the superconducting su(2) part of the global symmetry Lie algebra su(2)⊗su(2)/openZ2, holding at half filling for the customary model, into a quantum [su(2)]q symmetry, holding for a filling which depends on the electron-phonon interaction strength. Such symmetry originates in the feature that in the presence of phonons the hopping amplitude turns out to depend on the coupling strength. The states generated by resorting to this q symmetry exhibit both off-diagonal long-range order and pairing.