Phase transition from localization to chaos in a classical many-body system

We report a dynamical phase transition in the information spreading within a classical 2D deterministic interacting many-body system. Specifically, the transition is observed in a recently introduced momentum-conserving parity check cellular automaton (MCPCA) on the square lattice [Kasim and Prosen, ]. We characterize the transition using information-theoretic quantities such as the Hamming distance and the classical decorrelator. By introducing conserved local charges of the momentum-conserving parity-check cellular automata, we show that selecting initial ensembles with specific charge values allows the system to transition from a localized information phase to a chaotic regime with ballistic information spreading. Importantly, our findings indicate that this transition is of second order, highlighting a sharp change in information spreading behavior. Furthermore, we revisit the multifractal behavior of the dynamical structure factor and show that, although present across both phases, it originates from effective local periodicities enforced by symmetry constraints.