Dense gaps and scaling relations in the interacting Aubry-Andre' model

TL;DR

This paper rigorously analyzes the interacting Aubry-Andre' model, demonstrating that spectral gaps persist under weak interactions and are renormalized according to exact scaling relations, revealing deep insights into many-body effects.

Contribution

It provides a rigorous proof that spectral gaps in the Aubry-Andre' model remain open under weak interactions, with their widths governed by precise scaling laws.

Findings

Spectral gaps persist with weak interactions

Gap widths are renormalized by critical exponents

Scaling relations for gaps are verified

Abstract

We study, by rigorous Renormalization Group methods, the interacting Aubry-Andre' model for fermions in the extended regime. We show that the infinitely many gaps of the single particle spectrum persist in presence of weak many body interactions, despite the presence of Umklapp large momentum processes connecting the Fermi points. The width of the gaps is strongly renormalized through critical exponents which verify exact scaling relations.