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We generalize the Schrieffer-Wolff transformation to periodically drivensystems using Floquet theory. The method is applied to the periodically driven,strongly interacting Fermi-Hubbard model, for which we identify two regimesresulting in different effective low-energy Hamiltonians. In the nonresonantregime, we realize an interacting spin model coupled to a static gauge fieldwith a nonzero flux per plaquette. In the resonant regime, where the Hubbardinteraction is a multiple of the driving frequency, we derive an effectiveHamiltonian featuring doublon association and dissociation processes. Theground state of this Hamiltonian undergoes a phase transition between anordered phase and a gapless Luttinger liquid phase. One can tune the systembetween different phases by changing the amplitude of the periodic drive.

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields