Floquet prethermalization in periodically driven classical spin systems

It is proved that the energy absorption in a periodically driven classical spin system is exponentially slow in frequency, which results in a two-step relaxation called the Floquet prethermalization. This result is shown by establishing the classical limit of the quantum spin dynamics. The Floquet prethermal state is well described by the Gibbs ensemble with respect to the static effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion. On the other hand, the same effective Hamiltonian does not reproduce the local dynamics for an exponentially long time. This is due to the chaoticity of classical dynamics, and in stark contrast to quantum spin systems, in which the effective Hamiltonian well reproduces the exact quantum dynamics up to an exponentially long time.