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arXiv:2508.05381 · Physical review. B./Physical review. B

Random displacements in critical Rydberg atom arrays

Xingyu Li, Shuyan Zhou, Xue Chen, Chengshu Li, Hanteng Wang

Published Nov 21, 2025• 3 citations
arXivHTMLPDF

Abstract

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 ${\mathbb{Z}}_{2}$ 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 ${\mathbb{Z}}_{2}$-breaking perturbation. Our findings uncover disorder-driven phenomena and underscore the importance of carefully treating disorder effects in quantum simulators.

DOI
10.1103/dpn8-63p6

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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.
Chains of Rydberg atoms have emerged as a powerful platform for exploring low-dimensional quantum physics. This success originates from the precise control of lattice geometries provided by optical tweezers, which allows access to a wide range of synthetic quantum phases. Experiments on one-dimensional arrays have stimulated tremendous progress in understanding quantum phase transitions into crystalline phases. However, the finite width of tweezers introduces small variations in interatomic distances, leading to quenched disorder in the interactions. In this Letter, we numerically study how such disorder alters the nature of two critical regimes observed in experiments. First, following experimental protocols, we analyze Kibble-Zurek dynamics and find a crossover from the clean Ising transition to the infinite-randomness fixed point as system size and disorder strength increase. Second, we show that the floating phase-an incommensurate Luttinger liquid phase emerging at stronger interactions-is localized by the disorder, yet preserves short-range incommensurate correlations with the same leading wave vector. Our results clearly reveal an additional conceptual challenge in understanding critical phenomena using Rydberg-based quantum simulators.
Rydberg atom arrays have become a key platform for studying quantum many-body systems. In these setups, defects arise naturally due to various imperfections and can significantly modify the theoretical predictions compared to an ideal model. Here, we investigate the impact of geometric defects in the simplest situation---a one-dimensional Rydberg atom array, both at and away from its emergent Ising criticality. In the presence of defects, we demonstrate that relevant physical quantities can be extracted from one-point correlation functions. At the critical point, we show that different types of kinks yield distinct outcomes corresponding to their respective spatial-internal symmetries: site-centered kinks can effectively break the array at the kink position regardless of the kink angle, while bond-centered kinks lead to interesting intermediate-coupling fixed points. In the latter case, due to a special renormalization group flow trajectory, the whole system can appear ordered if the system is not large enough. Additionally, away from criticality, the bond-centered kink induces a localization-delocalization transition of the domain wall, characteristic of quantum wetting. These findings highlight the utility of kinks as experimental probes and stress the importance of controlling defects so that experimental observations remain faithful to the pristine model.
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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.
A programmable quantum simulator using Rydberg-atom array provides a promising route to demystifying quantum many-body physics in strongly correlated systems. Motivated by the recent realization of various quantum magnetic phases on the frustrated Rydberg-atom array, we perform numerically exact quantum Monte Carlo simulations to investigate the exotic states of matter emerging in the model describing the Rydberg atom on a triangular lattice. Our state-of-the-art simulation unveils the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ triangular antiferromagnetic order exists at 1/31/31/3 or 2/32/32/3-Rydberg filling, consistent with the observation in experiments. Remarkably, $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ long-range order arising from order-by-disorder mechanism emerges at 1/21/21/2 filling. At finite temperature, U(1)\mathrm{U}(1)U(1) symmetry is emergent at 1/21/21/2 filling and a Kosterlitz-Thouless phase transition occurs with increasing temperature. These intriguing phenomena are potentially detected in future Rydberg-atom experiments.
Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.