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Bound states of two interacting particles moving on a lattice can exhibitremarkable features that are not captured by the underlying single-particlepicture. Inspired by this phenomenon, we introduce a novel framework by whichgenuine interaction-induced geometric and topological effects can be realizedin quantum-engineered systems. Our approach builds on the design of effectivelattices for the center-of-mass motion of two-body bound states(\emph{doublons}), which can be created through long-range interactions. Thisgeneral scenario is illustrated on several examples, where flat-bandlocalization, topological pumps and higher-order topological corner modesemerge from genuine interaction effects. Our results pave the way for theexploration of interaction-induced topological effects in a variety ofplatforms, ranging from ultracold gases to interacting photonic devices.

Interaction-induced lattices for bound states: Designing flat bands, quantized pumps and higher-order topological insulators for doublons