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