Soliton pumping in the Rice-Mele model with on-cell Kerr nonlinearity

We investigate the Rice-Mele model with on-cell Kerr-type nonlinearities, where the interaction depends on the total particle number within each unit cell rather than on individual sites. This interaction enables a nontrivial interplay between topology and nonlinear dynamics in soliton pumping. In the weakly interacting regime, the ground-state soliton undergoes quantized Thouless pumping. At intermediate interaction strengths, soliton creation and annihilation break adiabaticity and disrupt quantized transport. In the strong-coupling regime, the coexistence of ground- and excited-state solitons leads to negligible coupling at energy crossings, giving rise to discrete time-translation symmetry breaking (DTTSB) in the soliton dynamics. Comparison of mean-field results with exact diagonalization along closed circular pumping paths confirms both the validity of the mean-field description and the robustness of DTTSB across different pumping trajectories. Our findings reveal how interaction-induced effects can fundamentally modify topological transport and suggest that these phenomena may be explored in cold-atom, photonic, and superconducting-circuit platforms.