Interaction-induced topological bound states and Thouless pumping in a one-dimensional optical lattice

We study topological features of interacting spin-12 particles in one-dimensional state-dependent optical lattices. Due to the cotranslational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound states appear as a result of the nontrivial center-of-mass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center of mass can be described by a nontrivial center-of-mass Chern number.