Hierarchy of many-body localized bound states in an interacting open lattice

We unveil the mechanism of the puzzling boundary-localized bound states formation in a spinless fermionic open lattice with nearest-neighbor interactions. By solving the Bethe-ansatz equation analytically, we uncover asymmetrical string solutions corresponding to the boundary-localized bound states, which emerge in systems with at least three particles. The localized bound states (LBSs) can become bound states in continuum with a suitably chosen parameter. When the number of particles increases to five or more, additional LBSs away from the boundary are also observed. Through rigorous analysis, we derive recurrence relations of the quasimomentum of the localized states as a function of the number of particles, predicting the presence of a hierarchy of many-body LBSs in interacting open lattices.