Small denominators and anomalous behaviour in the incommensurate Hubbard-Holstein model

We consider a system of interacting fermions on a chain in a periodic potential incommensurate with the chain spacing. We derive a convergent perturbative expansion, afflicted by a small denominator problem and based on renormalization group, for the two point Schwinger function. We obtain the large distance behavior of the Schwinger function, which is anomalous and described by critical indices, related to the gap and the wave function renormalization.