Interaction-induced splitting of Dirac monopoles in the topological Thouless pumping of strongly interacting Bosons and SU($N$) Fermions

Motivated by the observation of the breakdown of quantization for the Thouless pump in the presence of strong interaction [Walter et. al. Nat. Phys. (2023), Viebahn et. al. arXiv:2308.03756], we study the interplay of strong interaction and topology in the (1+1)-dimensional interacting Rice-Mele model. We point out that the quantization of the interacting Thouless pump is dictated by the Chern number, i.e., the Dirac monopoles enclosed by the generalized Brillouin zone of the many-body wave function. We analytically derive how interaction displaces the monopoles. Our model is applicable for arbitrary interaction strength and agrees with the mean-field approximation in the weak-interaction limit. Our predictions could be observed in strongly interacting SU($N$) Fermi gases or Bose gases in optical lattices and explain the ETH experiment on the pumping of strongly interacting SU(2) Fermi gases in 2023. In addition, we find interesting even-odd effects and unification of SU($N$) Fermi gases to $N$ bosons.