Small denominators and anomalous behaviour in the Holstein-Hubbard model

TL;DR

This paper develops a renormalization group-based perturbative expansion for an incommensurate fermionic chain, revealing anomalous large-distance behavior characterized by critical indices influenced by the gap and wave function renormalization.

Contribution

It introduces a convergent perturbative approach to analyze the Holstein-Hubbard model with small denominators, providing insights into its anomalous critical behavior.

Findings

Derived a convergent perturbative expansion for the two-point Schwinger function.

Identified anomalous large-distance decay governed by critical indices.

Linked the critical indices to the system's gap and wave function renormalization.

Abstract

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.