Double Butterfly Spectrum for Two Interacting Particles in the Harper Model

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 the noninteracting problem. Our numerical studies allow us to understand the global structure of the spectrum. An analytical approach developed permits us to understand the origin of localized states in the limit of strong interaction $U$ and fine spectral structure for small $U$.