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arXiv:2411.13643 · Physical Review Letters

Emergent Disorder and Sub-ballistic Dynamics in Quantum Simulations of the Ising Model Using Rydberg Atom Arrays

Ceren B. Dağ, Hanzhen Ma, P. Myles Eugenio, Fang Fang, Susanne F. Yelin

Published Nov 17, 2025• 5 citations
arXivHTMLPDF

Abstract

Rydberg atom arrays with van der Waals interactions provide a controllable path to quantum simulate the locally connected transverse-field Ising model (TFIM), a prototypical model in statistical mechanics. Remotely operating the publicly accessible Aquila Rydberg atom array, we experimentally investigate the physics of TFIM far from equilibrium and uncover significant deviations from the theoretical predictions. Rather than the expected ballistic spread of correlations, the Rydberg simulator exhibits a sub-ballistic spread, along with a logarithmic scaling of entanglement entropy in time all while the system mostly retains its initial magnetization. By modeling the atom motion, we trace these effects to an emergent disorder in Rydberg atom arrays, which we characterize with a minimal random spin model. We further experimentally explore the different dynamical regimes hosted in the system by varying the lattice spacing and the Rabi frequency. Our findings highlight the crucial role of atom motion in the many-body dynamics of Rydberg atom arrays at the TFIM limit, and propose simple benchmark measurements to test for its presence in future experiments.

DOI
10.1103/jr7l-2cfb

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Rydberg atom arrays with van der Waals interactions provide a controllable path to quantum simulate the locally connected transverse-field Ising model (TFIM), a prototypical model in statistical mechanics. Remotely operating the publicly accessible Aquila Rydberg atom array, we experimentally investigate the physics of TFIM far from equilibrium and uncover significant deviations from the theoretical predictions. Rather than the expected ballistic spread of correlations, the Rydberg simulator exhibits a sub-ballistic spread, along with a logarithmic scaling of entanglement entropy in time all while the system mostly retains its initial magnetization. By modeling the atom motion, we trace these effects to an emergent disorder in Rydberg atom arrays, which we characterize with a minimal random spin model. We further experimentally explore the different dynamical regimes hosted in the system by varying the lattice spacing and the Rabi frequency. Our findings highlight the crucial role of atom motion in the many-body dynamics of Rydberg atom arrays at the TFIM limit, and propose simple benchmark measurements to test for its presence in future experiments.
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Rydberg atom arrays promise high-fidelity quantum simulations of critical phenomena with flexible geometries. Yet, experimental realizations inevitably suffer from disorder due to random displacements of atoms, leading to departures from the expected behavior. Here, we study how such positional disorder influences the Ising criticality. Since disorder breaks the Z2{\mathbb{Z}}_{2}Z2​ symmetry, one might expect the system to flow to an infinite-strength disordered fixed point, erasing all nontrivial critical features in low spatial dimensions. Remarkably, we find instead that disorder in Rydberg systems is subjected to nontrivial local constraints, making the physics markedly different from systems with more conventional spatially short-range correlated or long-range correlated disorder. This leads to new classes of criticalities even at dimensions where conventional disorder would destroy criticality altogether. We then demonstrate as a consequence how a pseudocriticality emerges in Rydberg atom chains of experimentally realistic scale, and show that the renormalization group flow is governed by a locally constrained Z2{\mathbb{Z}}_{2}Z2​-breaking perturbation. Our findings uncover disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.
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The transient regime of far-from-equilibrium quantum many-body dynamics lacks the established organizing principles that universality and scaling provide in equilibrium. It is least understood for two-dimensional short-range interacting systems, where mean-field arguments are not expected to hold, controlled theoretical descriptions are few, and fluctuations are strong. Here we investigate the quench dynamics of the transverse-field Ising model using programmable Rydberg-atom arrays realizing honeycomb, square, kagome, and triangular lattices. Starting from a fully magnetized state, we observe a pronounced softening of the dominant collective magnetization oscillation accompanied by a maximum in the damping rate, signaling a crossover between interaction- and field-dominated transient dynamics. Even though the microscopic lattice geometries are different, both the oscillation frequencies and the damping rates collapse onto common curves after being rescaled by the coordination-number-weighted interaction strength. Our findings show that a mean-field description effectively reproduces the magnetization oscillations. The importance of correlated quantum fluctuations is underlined by the failure of the discrete truncated Wigner approximation to predict the damping for strong interactions, while tree-tensor-network simulations reproduce the dynamics accurately. These results reveal a robust scaling regime governing the transient dynamics of short-range interacting two-dimensional quantum magnets. They reveal that the dominant transient dynamics is governed by a simple collective description despite the presence of strong quantum fluctuations --- an important insight in the quest to uncover organizing principles in far-from-equilibrium quantum matter.