Integrability breaking in cellular automata

Cellular automata have recently attracted much attention as testbeds where to explore the interplay of quantum chaos, integrability, and hydrodynamics. In this work we study the Rule 54 model, perhaps the simplest non-trivial quantum integrable model, which features two species of solitons. On the first part of the talk I will show how the recently developed generalized hydrodynamics (GHD) framework allows us to analytically calculate transport coefficients which we verify by means of first-principle numerical simulations. In the second part of the talk I will show how the breaking of integrability in the model can lead to a crossover from the standard Boltzmann-type exponential relaxation at short times to anomalous transport at intermediate times.