It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states (such as bound states) in interacting quantum systems. Here, by introducing the cotranslational symmetry in an interacting multiparticle quantum system, we develop a method to define a Chern invariant, which is a generalization of the well-known Thouless-Kohmoto-Nightingaleden Nijs invariant, for identifying strongly interacting topological states. By using this topological invariant associated with the cotranslational symmetry, we explore several novel multiparticle topological states in strongly interacting systems, such as,

(i) topological magnon bounds states in a generalized two-dimensional Heisenberg XXZ model,

(ii) topological magnon bound states in a periodically modulated one-dimensional Heisenberg XXZ chains, and

(iii) Thouless pumping in an interacting Rice-Mele model of bosons.

Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

[1] X. Qin, F. Mei, Y. Ke, L. Zhang, C. Lee, Topological magnon bound-states in periodically modulated Heisenberg XXZ chains, arXiv:1602.03217

[2] X. Qin, F. Mei, Y. Ke, Li Zhang, C. Lee, Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems, arXiv:1611.00205

[3] Y. Ke, X. Qin, Y. Kivshar, C. Lee, Multi-particle Wannier states and Thouless pumping of interacting bosons, Phys. Rev. A 95, 063630 (2017).