Two interacting Hofstadter butterflies

TL;DR

This paper investigates the spectral properties and eigenstates of two interacting particles in a quasiperiodic potential, revealing an interaction-induced localization effect through analytical and numerical methods.

Contribution

It introduces a semiclassical approach using non-commutative geometry to analyze the complex spectrum of interacting particles in quasiperiodic systems.

Findings

Identification of an interaction-induced localization effect

Spectral analysis from weak to strong interactions

Application to a 2D model with magnetic field

Abstract

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on non commutative geometry techniques permits to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction.