Flow equation approach to Floquet systems
This event is part of the Biophysics/Condensed Matter Seminar Series.
Recent years have seen rapid progress in our understanding of periodically driven quantum systems. Even so many of the available theoretical techniques are still perturbative in nature or limited to certain classes of quantum systems - such as non-interacting or few site interacting systems. In this talk I will present a quite general 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 and driving strength regimes that are usually inaccessible via high frequency expansions. I will demonstrate how this approach can be applied to periodically driven many-body Hamiltonians. Using exact diagonalization as a benchmark we find that it offers an improvement over the more well-known Floquet-Magnus expansion. I will also demonstrate how the method is connected to an analog of Hamilton-Jacobi theory  and how this allows us to relate different common approximation techniques for time ordered exponentials. If time permits I will also briefly discuss lessons we learnt from our most recent work  on effective Hamiltonians for the low frequency, weak driving regime.  M. Vogl, P. Laurell, A. D. Barr, G. A. Fiete, “A flow equation approach to periodically driven systems”, Phys. Rev. X 9, 021037 (2019).  M. Vogl, P. Laurell, A. D. Barr, G. A. Fiete, “Analogue of Hamilton-Jacobi theory for the time-evolution operator”, Phys. Rev. A 100, 012132 (2019)  M. Vogl, M. Rodriguez-Vega, G. A. Fiete, “Effective Floquet Hamiltonian in the low-frequency regime”, arXiv:1909.04263