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We derive a systematic high-frequency expansion for the effective Hamiltonianand the micromotion operator of periodically driven quantum systems. Ourapproach is based on the block diagonalization of the quasienergy operator inthe extended Floquet Hilbert space by means of degenerate perturbation theory.The final results are equivalent to those obtained within a different approach[Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)]and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34},3379 (2000)]. We discuss that the dependence on the driving phase, whichplagues the latter, can lead to artifactual symmetry breaking. Thehigh-frequency approach is illustrated using the example of a periodicallydriven Hubbard model. Moreover, we discuss the nature of the approximation andits limitations for systems of many interacting particles.

High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective