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Systems subject to high-frequency driving exhibit Floquet prethermalization,that is, they heat exponentially slowly on a time scale that is large in thedrive frequency, $\tau_{\rm h} \sim \exp(\omega)$. Nonetheless, localobservables can decay much faster via energy conserving processes, which areexpected to cause a rapid decay in the fidelity of an initial state. Here weshow instead that the fidelities of eigenstates of the time-averagedHamiltonian, $H_0$, display an exponentially long lifetime over a wide range offrequencies -- even as generic initial states decay rapidly. When $H_0$ hasquantum scars, or highly excited-eigenstates of low entanglement, this leads tolong-lived non-thermal behavior of local observables in certain initial states.We present a two-channel theory describing the fidelity decay time $\tau_{\rmf}$: the interzone channel causes fidelity decay through energy absorption i.e.coupling across Floquet zones, and ties $\tau_{\rm f}$ to the slow heating timescale, while the intrazone channel causes hybridization between states in thesame Floquet zone. Our work informs the robustness of experimental approachesfor using Floquet engineering to generate interesting many-body Hamiltonians,with and without scars.

Prethermal stability of eigenstates under high frequency Floquet driving