We have studied an infinite Hubbard chain with a spin-orbit coupling term, submitted to a uniform magnetic field as well as local phonons. By means of a Lang-Firsov transformation, we show that an effective interacting fermion model emerges. Moreover, a self-consistent mean-field theory of this model,
formulated in terms of thermal Green's functions,
shows that a BCS term emerges, thus leading to a superconducting phase transition at zero temperature. We find analytical expressions for the phase boundary, that agree well with exact numerical diagonalization of the Hamiltonian.
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