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arXiv:2512.12695 · Physical Review A

Probing the Crossover between Dynamical Phases with Local Correlations in a Rydberg Atom Array

Xiaofeng Wu, Xin Wang, Sixun Jia, Bo Xiong

cond-mat.quant-gasquant-phSubmitted Dec 14, 2025• Announced Dec 16, 2025• 0 citations
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Abstract

The experimental detection of non-equilibrium quantum criticality remains a challenge, as traditional signatures like dynamical quantum phase transitions rely on hard-to-measure global properties. Here, we demonstrate that local connected correlation functions provide a superior, practical means to directly probe the dynamics of magnetic order in a quenched Rydberg atom array. Using a Magnus expansion formalism, we derive analytic expressions for these correlations that capture a smooth crossover from antiferromagnetic to ferromagnetic dominance. Our analytic results, which reveal the critical parameter relationship $U_{c}(δ)$, are validated against exact numerical simulations and exhibit robustness to finite-size effects. By shifting the focus from global singularities to local correlations, our protocol establishes a direct and feasible path to observe the rich critical dynamics in scalable quantum simulators.

Journal reference
Phys. Rev. A 113, 062204 (2026)
DOI
10.1103/3qxv-jc14
Comments
6+9 pages, 4+2 figures

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The experimental detection of non-equilibrium quantum criticality remains a challenge, as traditional signatures like dynamical quantum phase transitions rely on hard-to-measure global properties. Here, we demonstrate that local connected correlation functions provide a superior, practical means to directly probe the dynamics of magnetic order in a quenched Rydberg atom array. Using a Magnus expansion formalism, we derive analytic expressions for these correlations that capture a smooth crossover from antiferromagnetic to ferromagnetic dominance. Our analytic results, which reveal the critical parameter relationship Uc(δ)U_{c}(δ)Uc​(δ), are validated against exact numerical simulations and exhibit robustness to finite-size effects. By shifting the focus from global singularities to local correlations, our protocol establishes a direct and feasible path to observe the rich critical dynamics in scalable quantum simulators.
Understanding the mechanism behind the buildup of inner correlations is crucial for studying nonequilibrium dynamics in complex, strongly interacting many-body systems. Here we investigate both analytically and numerically the buildup of antiferromagnetic (AF) correlations in a dynamically tuned Ising model with various geometries, realized in a Rydberg atomic system. Through second-order Magnus expansion (ME), we demonstrate quantitative agreement with numerical simulations for diverse configurations including 2 × n 2 × n lattice and cyclic lattice with a star. We find that the AF correlation magnitude at fixed Manhattan distance obeys a universal superposition principle: It corresponds to the algebraic sum of contributions from all shortest paths. This superposition law remains robust against variations in path equivalence, lattice geometries, and quench protocols, establishing a new paradigm for correlation propagation in quantum simulators.
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The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
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Extracting critical behavior in the wake of quantum quenches has recently been at the forefront of theoretical and experimental investigations in condensed matter physics and quantum synthetic matter, with particular emphasis on experimental feasibility. Here, we investigate the potential of single-site observables in probing equilibrium phase transitions and dynamical criticality in short-range transverse-field Ising chains. For integrable and near-integrable models, our exact and mean-field-theory analyses reveal a truly out-of-equilibrium universal scaling exponent in the vicinity of the transition that is independent of the initial state and the location of the probe site so long as the latter is sufficiently close to the edge of the chain. Signature of a dynamical crossover survives when integrability is strongly broken. Our work provides a robust scheme for the experimental detection of quantum critical points and dynamical scaling laws in short-range interacting models using modern ultracold-atom setups.
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.