Stochastic Semi-Classical Models of Operator Front Dynamics

The growth in size and complexity of generic local operators due to unitary time evolution has been studied for numerous quantum models and using a variety of theoretical techniques. The operator-front spreads ballistically, and in the limit of late times has a universal "hydrodynamic" description. For a class of quantum models, we provide evidence for an effective classical description of this hydrodynamic behavior that can be simulated efficiently using models of "cellular automata" (CA). Starting with a few elementary CA rules we demonstrate the emergence of distinct universality classes of operator-front hydrodynamics, which leads to complementary insight into the dynamics of quantum many-body systems.