  We present a Floquet Schrieffer Wolff transform (FSWT) to obtain effective
Floquet Hamiltonians and micro-motion operators of periodically driven
many-body systems for any non-resonant driving frequency. The FSWT
perturbatively eliminates the oscillatory components in the driven Hamiltonian
by solving operator-valued Sylvester equations. We show how to solve these
Sylvester equations without knowledge of the eigenstates of the undriven
many-body system, using the driven Hubbard model as an example. In the limit of
high driving frequencies, these solutions reduce to the well-known
high-frequency limit of the Floquet-Magnus expansion. We anticipate this method
will be useful for describing multi-orbital and long-range interacting systems
driven in-gap.
