  We study topological features of interacting spin- 1 2 particles in
one-dimensional state-dependent optical lattices. Due to the co-translational
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 non-trivial center-ofmass 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 non-trivial
center-of-mass Chern number.
