  Quantum phases and their transitions play a pivotal role to characterize
macroscopic matter. Recent studies have revealed that critical transitions
reminiscent of equilibrium phase transitions can occur even out of equilibrium,
as a singularity of dynamical counterpart of free energy. In this paper, we
report a novel mechanism of dynamical phase transitions caused by spontaneous
hidden antiunitary-symmetry breaking in periodically driven unitary dynamics.
We characterize dynamical phases in such systems with nonunitary many-body
operator obtained by switching space and time and find that its symmetry
constrains the nature of phases and their transitions. In particular, at some
parameters of stroboscopic Ising models, dynamical free energy density exhibits
a critical transition with novel singularity absent in equilibrium. The
criticality and its universal exponent originate from a many-body exceptional
point of the nonunitary operator associated with spontaneous
antiunitary-symmetry breaking. We also show that the generalized correlation
function has the divergent correlation length at transition and exhibits
oscillatory long-range order after symmetry breaking. Our results open up a
quest for hitherto unknown phases with their hidden connection to nonunitary
physics in macroscopic nonequilibrium systems, which can be tested in
state-of-the-art quantum simulators.
