  Extending notions of phase transitions to nonequilibrium realm is a
fundamental problem for statistical mechanics. While it was discovered that
critical transitions occur even for transient states before relaxation as the
singularity of a dynamical version of free energy, their nature is yet to be
elusive. Here, we show that spontaneous symmetry breaking can occur at a
short-time regime and causes universal dynamical quantum phase transitions in
periodically driven unitary dynamics. Unlike conventional phase transitions,
the relevant symmetry is antiunitary: its breaking is accompanied by a
many-body exceptional point of a nonunitary operator obtained by space-time
duality. Using a stroboscopic Ising model, we demonstrate the existence of
distinct phases and unconventional singularity of dynamical free energy, whose
signature can be accessed through quasilocal operators. Our results open up
research for hitherto unknown phases in short-time regimes, where time serves
as another pivotal parameter, with their hidden connection to nonunitary
physics.
