Exact Nonequilibrium Dynamics and Hidden Markov Order in Floquet-PXP Quantum Cellular Automaton

Studies of integrable models have profoundly deepened the fundamental understanding of quantum many-body systems, while accurate characterizations of nonequilibrium dynamics of them remain a significant challenge. In this talk, I will report recent progress on exact dynamics of the "Rule 201" quantum cellular automaton, which realizes an integrable Trotterization of the PXP Hamiltonian. I will display a rich landscape of dynamics using the tensor-network approach of the influence matrix. That includes non-thermal relaxation of persistent oscillating dynamics under local perturbations with analytical solutions, and thermalizing behavior supported by numerically exact results. I will further demonstrate a refined structure of multitime correlations admitting decompositions into finite-length and long-range distributed components, termed the hidden Markov order. These findings unify nonthermalizing and thermalizing dynamics within a single analytically tractable model, and can be tested in advanced experimental platforms such as Rydberg atom arrays.