q-Symmetry in Condensed Matter Physics: an Effective Generalized Hubbard Model with Quantum Symmetry

Using the generalized Lang–Firsov transformation, we reduce the Hubbard model with phonons (which, under particular circumstances, has recently been shown to exhibit the quantum symmetry su(2) ⊕ [su(2)]q ) into an effective electron Hamiltonian. The effective Hamiltonian is explicitly proved to maintain the quantum symmetry, which survives even when relaxing one of the constraints on the Hamiltonian parameters that must hold in the model with phonons. We investigate under which circumstances some superconducting eigenstates of the effective Hamiltonian, which can be built thanks to the quantum symmetry, could become metastable.