  The presence of quantum scars, athermal eigenstates of a many-body
Hamiltonian with finite energy density, leads to absence of ergodicity and
long-time coherent dynamics in closed quantum systems starting from simple
initial states. Such non-ergodic coherent dynamics, where the system does not
explore its entire phase space, has been experimentally observed in a chain of
ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg
chain, that the drive frequency acts as a tuning parameter for several
reentrant transitions between ergodic and non-ergodic regimes. The former
regime shows rapid thermalization of correlation functions and absence of scars
in the spectrum of the system's Floquet Hamiltonian. The latter regime, in
contrast, has scars in its Floquet spectrum which control the long-time
coherent dynamics of correlation functions. Our results open a new possibility
of drive frequency-induced tuning between ergodic and non-ergodic dynamics in
experimentally realizable disorder-free quantum many-body systems.
