Fast quantum-state transfer in Su-Schrieffer-Heeger chains beyond the noninteracting regime

Shortcuts to adiabaticity have made topological edge-state transfer fast in the single-particle regime, but their extension to interacting systems is obstructed by nonlinear phase accumulation. We show that this obstruction can be removed in Su-Schrieffer-Heeger chains by making the next-nearest-neighbor shortcut hopping phase tunable. In the mean-field regime, this yields an exact nonlinear shortcut: one hopping quadrature keeps the state on the instantaneous dark-state trajectory, while the orthogonal quadrature cancels the interaction-induced self-phase modulation. The resulting protocol is nonperturbative in the mean-field interaction strength. When applied to the full Bose-Hubbard dynamics, the mean-field shortcut remains beneficial but saturates below unit fidelity, exposing genuinely many-body corrections beyond the product-state picture. We then optimize the transfer directly in the many-body Hilbert space and find that complex, phase-tunable next-nearest-neighbor hoppings recover near-perfect fidelity. Our results show that hopping phases are not merely a technical refinement, but a key control resource for fast and high-fidelity transport in interacting topological systems.