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We study theoretically quantum states of two repelling spinless particles ina one-dimensional tight-binding model with simple periodic lattice and openboundary conditions. We demonstrate, that when the particles are not identical,their interaction drives nontrivial correlated two-particle states, such asbound states, edge states as well as interaction-induced flat bands.Specifically, the center-of-mass and relative motions of two particles becomecoupled in a topologically nontrivial way. By virtue of the non-Hermitian skineffect the localization of the center of mass enforces the localization of therelative motion and formation of the bound states.

Topologically bound states, non-Hermitian skin effect and flat bands, induced by two-particle interaction