  The PXP model hosts a special set of nonergodic states, referred to as
quantum many-body scars. One of the consequences of quantum scarring is the
periodic revival of the wave function fidelity. It has been reported that
quantum fidelity revival occurs in the PXP model for certain product states,
and periodic driving of chemical potential can enhance the magnitude of quantum
revival, and can even change the frequencies of revival showing the subharmonic
response. Although the effect of the periodic driving in the PXP model has been
studied in the limit of certain perturbative regimes, the general mechanism of
such enhanced revival and frequency change has been barely studied. In this
work, we investigate how periodic driving in the PXP model can systematically
control the fidelity revival. Particularly, focusing on the product state so
called a Neel state, we analyze the condition of driving to enhance the
magnitude of revival or change the frequencies of revival. To clarify the
reason of such control, we consider the similarities between the PXP model and
the free spin-1/2 model in graph theoretical analysis, and show that the
quantum fidelity feature in the PXP model is well explained by the free
spin-1/2 model. In addition, under certain limit of the driving parameters,
analytic approach to explain the main features of the fidelity revival is also
performed. Our results give an insight of the scarring nature of the
periodically driven PXP model and pave the way to understand their
(sub-)harmonic responses and controls.
