Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model

• URL: http://arxiv.org/abs/2606.19430v1
• Date: Wed, 17 Jun 2026 18:00:01 GMT
• Title: Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model
• Abstract summary: "Rule 201" quantum cellular automaton is an integrable Trotterization of the PXP Hamiltonian.<n>We develop local conditions called generalized zipper conditions that allow exact solutions of local dynamics.<n>This uncovers a rich landscape of nonequilibrium behavior exhibiting initial-state dependence.
• Score: 3.108119331549279
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Studies of integrable systems have profoundly deepened the fundamental understanding of quantum many-body physics. While equilibrium properties such as ground states and thermodynamics can often be characterized efficiently, accurately characterizing nonequilibrium integrable dynamics remains a significant challenge. Here, we address this problem in the "Rule 201" quantum cellular automaton, an integrable Trotterization of the PXP Hamiltonian. Using the tensor-network approach of the influence matrix, we develop local conditions called generalized zipper conditions that allow exact solutions of local dynamics. We also introduce a numerical bootstrap method for solving influence matrices with finite but relatively large bond dimensions. This uncovers a rich landscape of nonequilibrium behavior exhibiting initial-state dependence. As an example, we investigate the fate of persistent oscillating dynamics under local non-integrable perturbations, and present analytical results for non-thermal relaxation constrained by conservation laws. We also obtain numerically exact results for entanglement growth across a broad class of initial states. Furthermore, from an information-theoretic perspective, we identify a refined structure of multitime correlations termed the hidden Markov order: the memory encoded in the dynamics separates into finite-length and long-range distributed components, which becomes transparent in an exact split-index matrix-product-state representation of the influence matrix. Our approach enables unified investigations of nonthermalizing and thermalizing regimes of nonequilibrium dynamics within a single analytically tractable model, and can be tested experimentally in state-of-the-art quantum simulators such as Rydberg atom arrays.

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