  The far-from-equilibrium dynamics of generic interacting quantum systems is
characterized by a handful of universal guiding principles, among them the
ballistic spreading of initially local operators. Here, we show that in certain
constrained many-body systems the structure of conservation laws can cause a
drastic modification of this universal behavior. As an example, we study
operator growth characterized by out-of-time-order correlations (OTOCs) in a
dipole-conserving fracton chain. We identify a critical point with
sub-ballistically moving OTOC front, that separates a ballistic from a
dynamically frozen phase. This critical point is tied to an underlying
localization transition and we use its associated scaling properties to derive
an effective description of the moving operator front via a biased random walk
with long waiting times. We support our arguments numerically using classically
simulable automaton circuits.
