Two-body bound and edge bound states in a ladder lattice with synthetic flux

We study the composite nature of two interacting bosons in the presence of a uniform synthetic flux on a two-leg ladder. We identify the existence of in-cell two-body bound states and nearest-neighbor bound pairs. Under open boundary condition, edge states associated to the bound spectra arise even for the chiral ladder that is topological trivial. We present effective models to characterize the appearance of bound states, as well as to capture the localization and chiral properties of the edge bound state (EBS). Moreover, we incorporate the diagonal coupling into the ladder, constituting a Creutz model which supports topological phase transition. We show that the interplay of non-trivial band topology and the two-body interaction leads to topological EBS that is robust against local potential defect.