  The most typical ingredient of topologically protected quantum states are
magnetic fluxes. In a system of spins, complex-valued interaction parameters
give rise to a flux, if their phases do not add up to zero along a closed loop.
Here we apply periodic driving, a powerful tool for quantum engineering, to a
trapped-ion quantum simulator in order to generate such spin-spin interactions.
We consider a simple driving scheme, consisting of a repeated series of locally
quenched fields, and demonstrate the feasibility of this approach by studying
the dynamics of a small system. An emblematic hallmark of the flux, accessible
in experiments, is the appearance of chiral spin currents. Strikingly, we find
that in parameter regimes where, in the absence of fluxes, phonon excitations
dramatically reduce the fidelity of the spin model simulation, the spin
dynamics remains widely unaffected by the phonons when fluxes are present.
