Flow equation approach to periodically driven quantum systems

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