Quantum theory of (fractional) topological transport of lattice solitons

We show that the transport of bound N-particle composite objects in a lattice / lattice solitons upon adiabatic changes of the Hamiltonian is determined by the effective single-particle band-structure of the center-of-mass (COM) motion, which has a dynamical and a topological contribution. The topological contribution is characterized by a Chern number. Changing the interaction energy leads to a successive merging of COM bands resulting in topological phase transitions from phases with integer quantized transport through different phases of fractional transport, characterized by a non-trivial Wilson loop, to a phase without topological transport. For a minimal model of three strongly interacting particles we explicitly construct the effective single-particle Hamiltonian of the bound triplon which shows a transition from a fractional quantized transport to a localized phase.