Long-time behavior of periodically driven isolated interacting lattice systems

We study the dynamics of isolated interacting spin chains that are periodically driven by sudden quenches. Using full exact diagonalization of finite chains, we show that these systems exhibit three distinct regimes. For short driving periods, the Floquet Hamiltonian is well approximated by the time-averaged Hamiltonian, while for long periods the evolution operator exhibits properties of random matrices of a Circular Ensemble (CE). In-between, there is a crossover regime. Based on a finite-size scaling analysis and analytic arguments we argue that, for thermodynamically large systems and non-vanishing driving periods, the evolution operator always exhibits properties of CE random matrices. Consequently, the Floquet Hamiltonian is nonlocal and has multi-body interactions; and the driving leads to the equivalent of an infinite temperature state at long times. These results are connected to the breakdown of the Magnus expansion and are expected to hold beyond the specific lattice model considered.