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A Thouless pump transports an integer amount of charge when pumpingadiabatically around a singularity. We study the splitting of such a criticalpoint into two separate critical points by adding a Hubbard interaction.Furthermore, we consider extensions to a spinful Rice-Mele model, namely astaggered magnetic field or an Ising-type spin coupling, further reducing thespin symmetry. The resulting models additionally allow for the transport of asingle charge in a two-component system of spinful fermions, whereas in theabsence of interactions, zero or two charges are pumped. In the SU(2)-symmetriccase, the ionic Hubbard model is visited once along pump cycles that enclose asingle singularity. Adding a staggered magnetic field additionally transportsan integer amount of spin while the Ising term realizes a pure charge pump. Weemploy real-time simulations in finite and infinite systems to calculate theadiabatic charge and spin transport, complemented by the analysis of gaps andthe many-body polarization to confirm the adiabatic nature of the pump. Theresulting charge pumps are expected to be measurable in finite-pumping speedexperiments in ultra-cold atomic gases, for which the SU(2) invariant versionis the most promising path. We discuss the implications of our results for arelated quantum-gas experiment by Walter et al. [arXiv:2204.06561].

Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model