Double butterfly spectrum for two interacting particles in the Harper model

TL;DR

This paper investigates how interparticle interactions influence the spectrum of the Harper model, revealing the emergence of localized states and complex spectral structures through numerical and analytical methods.

Contribution

It introduces a detailed analysis of the spectral effects of interactions in the Harper model, including the origin of localized states and multifractal spectrum features.

Findings

Interaction $U$ induces a pure-point spectrum component.

Localized states emerge in the strong interaction limit.

Spectral structure varies significantly with interaction strength.

Abstract

We study the effect of interparticle interaction $U$ on the spectrum of the Harper model and show that it leads to a pure-point component arising from the multifractal spectrum of non interacting problem. Our numerical studies allow to understand the global structure of the spectrum. Analytical approach developed permits to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.