  Prethermalization, by introducing emergent quasiconserved observables, plays
a crucial role in protecting Floquet many-body phases over exponentially long
time, while the ultimate fate of such quasiconserved operators can signal
thermalization to infinite temperature. To elucidate the properties of
prethermal quasiconservation in many-body Floquet systems, here we
systematically analyze infinite temperature correlations between observables.
We numerically show that the late-time behavior of the autocorrelations
unambiguously distinguishes quasiconserved observables from non-conserved ones,
allowing to single out a set of linearly-independent quasiconserved
observables. By investigating two Floquet spin models, we identify two
different mechanism underlying the quasi-conservation law. First, we
numerically verify energy quasiconservation when the driving frequency is
large, so that the system dynamics is approximately described by a static
prethermal Hamiltonian. More interestingly, under moderate driving frequency,
another quasiconserved observable can still persist if the Floquet driving
contains a large global rotation. We show theoretically how to calculate this
conserved observable and provide numerical verification. Having systematically
identified all quasiconserved observables, we can finally investigate their
behavior in the infinite-time limit and thermodynamic limit, using
autocorrelations obtained from both numerical simulation and experiments in
solid state nuclear magnetic resonance systems.
