Induced gauge potentials in reduced density matrix dynamics

The combination of interactions and nonadiabaticity in many body systems is shown to induce magnetic gauge potentials in the equation of motion for the one-body reduced density matrix as well as the effective Schroedinger equation for the natural orbitals. The consequences of induced gauge geometry for charge and energy transfer are illustrated in the exact nonlinear dynamics of a three-site Hubbard ring ramped into a Floquet state by a time dependent circulating electric potential. Remarkably, the pumped charge flows against the driving in the strongly interacting regime, and the quasienergy level shift, which defines the work done on the system, can become negative.