A flow equation approach to periodically driven quantum systems

We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. The method has a range of validity reaching into frequency regimes that are usually inaccessible via high frequency expansions. Our approach is demonstrated for many-body Hamiltonians where it offers an improvement over the more well-known Magnus expansion. We show how the method relates to the rotating frame approximation and how it can be used to approximately transform to a rotating frame where the exact transformation isn't tractable because infinitely many couplings are generated in an exact treatment. We compare our approximate results to those found via exact diagonalization.