Two interacting Hofstadter butterflies
Armelle Barelli, Jean Bellissard, Philippe Jacquod, Dima L., Shepelyansky

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.
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