Eigenstate prethermalization*

Experimental advances in periodic driving fields allow for the manipulation of quantum phases of matter and the design of Floquet-engineered effective Hamiltonians. The driving, which breaks time translation invariance, ultimately thermalizes the system to a featureless infinite temperature state. Nevertheless, there are rigorous exponential-in-frequency bounds on the heating rates, allowing for nontrivial dynamics for long periods of time. While these bounds apply for global quasi-conservation laws such as energy, we show that even individual many-body eigenstates of a leading order effective Hamiltonian, $H_0$, show long-lived fidelity under the time evolution generated by the full, driven Hamiltonian.  Our results have promising implications for Floquet engineering, and are especially interesting when $H_0$ has outlier eigenstates, called scar states.