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In flat-band systems, destructive interference leads to the localization ofnon-interacting particles and forbids their motion through the lattice.However, in the presence of interactions the overlap between neighbouringsingle-particle localized eigenstates may enable the propagation of bound pairsof particles. In this work, we show how these interaction-induced hoppings canbe tuned to obtain a variety of two-body topological states. In particular, weconsider two interacting bosons loaded into the orbital angular momentum $l=1$states of a diamond-chain lattice, wherein an effective $\pi$ flux may yield acompletely flat single-particle energy landscape. In the weakly-interactinglimit, we derive effective single-particle models for the two-bosonquasiparticles which provide an intuitive picture of how the topological statesarise. By means of exact diagonalization calculations, we benchmark thesestates and we show that they are also present for strong interactions and awayfrom the strict flat-band limit. Furthermore, we identify a set of doublylocalized two-boson flat-band states that give rise to a special instance ofAharonov-Bohm cages for arbitrary interactions.

Interaction-induced topological properties of two bosons in flat-band systems