Floquet Schrieffer-Wolff transform based on Sylvester equations

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.