Two interacting Hofstadter butterflies
arXiv:cond-mat/9610182 · doi:10.1103/PhysRevB.55.9524
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.
revtex, 12 pages, 11 figures