  Motivated by experimental observations of time-symmetry breaking behavior in
a periodically driven (Floquet) system, we study a one-dimensional spin model
to explore the stability of such Floquet discrete time crystals (DTCs) under
the interplay between interaction and the microwave driving. For intermediate
interactions and high drivings, from the time evolution of both stroboscopic
spin polarization and mutual information between two ends, we show that Floquet
DTCs can exist in a prethermal time regime without the tuning of strong
disorder. For much weak interactions the system is a symmetry-unbroken phase,
while for strong interactions it gives its way to a thermal phase. Through
analyzing the entanglement dynamics, we show that large driving fields protect
the prethermal DTCs from many-body localization and thermalization. Our results
suggest that by increasing the spin interaction, one can drive the experimental
system into optimal regime for observing a robust prethermal DTC phase.
