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Two interacting Hofstadter butterflies

Armelle Barelli·Jean Bellissard·Philippe Jacquod·Dima L. Shepelyansky
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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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Armelle Barelli, Jean Bellissard, Philippe Jacquod, Dima L. Shepelyansky. 1996-10-25. Two interacting Hofstadter butterflies. https://doi.org/10.1103/physrevb.55.9524

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