  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.
