  Dynamical quantum phase transitions (DQPTs) at critical times appear as
non-analyticities during nonequilibrium quantum real-time evolution. Although
there is evidence for a close relationship between DQPTs and equilibrium phase
transitions, a major challenge is still to connect to fundamental concepts such
as scaling and universality. In this work, renormalization group
transformations in complex parameter space are formulated for quantum quenches
in Ising models showing that the DQPTs are critical points associated with
unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey
scaling and universality. On the basis of numerical simulations, signatures of
these DQPTs in the dynamical buildup of spin correlations are found with an
associated power-law scaling determined solely by the fixed point's
universality class. An outlook is given on how to explore this dynamical
scaling experimentally in systems of trapped ions.
