Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model
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 develop an influence matrix bootstrap approach for exactly solving nonequilibrium dynamics. This approach begins with an ansatz consisting of a set of local tensor relations, termed generalized zipper conditions, and uses finite-time data to construct exact solutions of local dynamics that extend to arbitrarily long times. We demonstrate this approach in the "Rule 201" quantum cellular automaton, an integrable Trotterization of the PXP Hamiltonian. 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 orde}: 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.
Related
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BibTeX
@misc{yang2026solving,
title = {{Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model}},
author = {Xiao-Yang Yang and He-Ran Wang and Zhong Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.19430},
eprint = {2606.19430},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19430},
}
RIS
TY - UNPB
TI - Solving Nonequilibrium Dynamics via Influence Matrix Bootstrap: Floquet-PXP Model
AU - Xiao-Yang Yang
AU - He-Ran Wang
AU - Zhong Wang
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2606.19430
UR - https://arxiv.org/abs/2606.19430
AB - 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 develop an influence matrix bootstrap approach for exactly solving nonequilibrium dynamics. This approach begins with an ansatz consisting of a set of local tensor relations, termed generalized zipper conditions, and uses finite-time data to construct exact solutions of local dynamics that extend to arbitrarily long times. We demonstrate this approach in the "Rule 201" quantum cellular automaton, an integrable Trotterization of the PXP Hamiltonian. 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 orde}: 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.
ER -