Interaction-induced analog of a non-Hermitian skin effect in a lattice two-body problem

We present a theoretical study of the quantum states of two repelling spinless particles in a one-dimensional tight-binding model with a 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 and edge states, and induces interaction-induced flat bands. We show that the localization of the center of mass of the two particles enforces the localization of their relative motion, which means formation of the bound states. While the considered system is Hermitian, an insight into the bound states is provided by an approximate effective non-Hermitian model for the relative motion that features the non-Hermitian skin effect.