  We study the real-time dynamics of a quantum Ising chain driven periodically
by instantaneous quenches of the transverse field (the transverse field varying
as rectangular wave symmetric about zero). Two interesting phenomena are
reported and analyzed: (1) We observe dynamical many-body freezing or DMF
(Phys. Rev. B, vol. 82, 172402, 2010), i.e. strongly non-monotonic freezing of
the response (transverse magnetization) with respect to the driving parameters
(pulse width and height) resulting from equivocal freezing behavior of all the
many-body modes. The freezing occurs due to coherent suppression of dynamics of
the many-body modes. For certain combination of the pulse height and period,
maximal freezing (freezing peaks) are observed. For those parameter values, a
massive collapse of the entire Floquet spectrum occurs. (2) Secondly, we
observe emergence of a distinct solitary oscillation with a single frequency,
which can be much lower than the driving frequency. This slow oscillation,
involving many high-energy modes, dominates the response remarkably in the
limit of long observation time. We identify this slow oscillation as the unique
survivor of destructive quantum interference between the many-body modes. The
oscillation is found to decay algebraically with time to a constant value. All
the key features are demonstrated analytically with numerical evaluations for
specific results.
