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arxiv: 2506.11985 · v3 · submitted 2025-06-13 · ❄️ cond-mat.str-el

Infinite randomness criticality and localization of the floating phase in arrays of Rydberg atoms trapped with non-perfect tweezers

Jose Soto-Garcia , Natalia Chepiga This is my paper

Pith reviewed 2026-05-19 09:23 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords Rydberg atomsquenched disorderinfinite randomnessfloating phaseKibble-Zurek dynamicsquantum phase transitionsoptical tweezersincommensurate correlations
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The pith

Disorder from imperfect tweezers replaces the clean Ising transition with infinite-randomness criticality in Rydberg atom chains and localizes the floating phase while preserving its short-range incommensurate correlations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper studies how small variations in atomic spacings from the finite width of optical tweezers introduce quenched disorder into one-dimensional Rydberg atom arrays. Following experimental Kibble-Zurek protocols, it finds that this disorder drives a crossover from the clean Ising critical point to an infinite-randomness fixed point as system size and disorder strength grow. It also shows that the floating phase, an incommensurate Luttinger liquid at stronger interactions, becomes localized yet retains short-range correlations with the original leading wave vector. These findings highlight a practical obstacle for using Rydberg platforms to study clean quantum critical phenomena.

Core claim

Numerical analysis of Kibble-Zurek dynamics in Rydberg chains with quenched disorder from non-perfect tweezers shows a crossover from the clean Ising transition to the infinite-randomness fixed point with increasing system size and disorder strength. The floating phase is localized by the disorder but preserves short-range incommensurate correlations with the same leading wave vector.

What carries the argument

Quenched disorder in interatomic interactions modeled from finite tweezer width, analyzed through Kibble-Zurek ramp protocols and correlation-function diagnostics to track the fixed-point crossover and phase localization.

If this is right

  • Larger experimental Rydberg arrays will display infinite-randomness rather than clean Ising scaling near the critical point.
  • The floating phase remains detectable in experiments through its short-range incommensurate correlations despite localization.
  • Theoretical models of Rydberg simulators must incorporate disorder to interpret critical phenomena correctly.
  • Similar localization effects may appear in other one-dimensional quantum simulators with position disorder.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This work suggests that many existing interpretations of Rydberg critical-point data may need revision once finite-size and disorder effects are included.
  • It opens the possibility that infinite-randomness fixed points are the generic outcome in realistic trapped-atom setups rather than an exotic limit.
  • Comparable disorder-induced localization could be tested in other platforms by engineering controlled spacing variations and measuring correlation functions.
  • The preserved short-range wave vector offers a route to identify the floating phase even when long-range order is destroyed.

Load-bearing premise

The numerical model of interaction variations caused by finite tweezer width accurately represents the disorder present in actual Rydberg-atom experiments.

What would settle it

Direct measurement of dynamical scaling exponents or correlation lengths in Rydberg arrays of increasing length under controlled tweezer imperfections to detect the crossover to infinite-randomness behavior.

Figures

Figures reproduced from arXiv: 2506.11985 by Jose Soto-Garcia, Natalia Chepiga.

Figure 1
Figure 1. Figure 1: Deviation from the clean power-law scaling in the Kibble-Zurek mechanism caused by the disorder. Density of kinks nk as a function of sweep rate s for multiple values of disorder strength δV = 0.15, 0.25, 0.4 for the system size L = 241. Results for the clean case (blue circles) are shown for the reference. The dashed grey line corresponds to the theoretical scaling for the Ising universality class. Error … view at source ↗
Figure 3
Figure 3. Figure 3: System size dependence of Kibble-Zurek [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Dependence of the Kibble-Zurek critical exponent on disorder strength and system size. The critical exponent µ is shown as a function of disorder strength δV for various system sizes. Error bars represent 95% confidence intervals derived from the covariance matrix of the fit. tem sizes, we plot 1/nk versus log2 (s) in [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Proximity of the transition to the infinte [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Probability distribution of kinks after a [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
read the original abstract

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. Firstly, 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. Secondly, 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript numerically investigates the effects of quenched disorder arising from finite optical tweezer widths on critical regimes in one-dimensional Rydberg atom arrays. Following experimental protocols, it reports a crossover from the clean Ising transition to the infinite-randomness fixed point in Kibble-Zurek dynamics as system size and disorder strength increase. It further shows that the floating phase is localized by the disorder while retaining short-range incommensurate correlations with the same leading wave vector.

Significance. If the numerical results hold under the modeled disorder, the work is significant for quantum simulation with Rydberg atoms. It identifies how realistic experimental imperfections drive systems toward infinite-randomness criticality and localize incommensurate phases, offering concrete implications for interpreting experiments and motivating disorder-inclusive theoretical models. The adherence to experimental protocols is a positive feature.

major comments (1)
  1. [Methods section on disorder generation and results for floating phase] The modeling of quenched disorder via independent position fluctuations from finite tweezer width (producing variations in the ~1/r^6 interactions) is load-bearing for both central claims. If the simulated distribution differs in spatial correlations, variance, or higher moments from actual experimental tweezer imperfections, the crossover to activated scaling in Kibble-Zurek dynamics and the localization of the floating phase (while preserving the wave vector) may not occur at the reported disorder strengths. This requires explicit validation or comparison in the methods section describing the disorder implementation.
minor comments (1)
  1. [Abstract] The abstract states that the floating phase 'preserves short-range incommensurate correlations with the same leading wave vector' but does not define how the wave vector is extracted or compared; a brief clarification or reference to the relevant figure/equation would aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: [Methods section on disorder generation and results for floating phase] The modeling of quenched disorder via independent position fluctuations from finite tweezer width (producing variations in the ~1/r^6 interactions) is load-bearing for both central claims. If the simulated distribution differs in spatial correlations, variance, or higher moments from actual experimental tweezer imperfections, the crossover to activated scaling in Kibble-Zurek dynamics and the localization of the floating phase (while preserving the wave vector) may not occur at the reported disorder strengths. This requires explicit validation or comparison in the methods section describing the disorder implementation.

    Authors: We thank the referee for highlighting the central role of the disorder model. In the manuscript we generate quenched disorder by assigning independent Gaussian position fluctuations to each atom, with the standard deviation chosen to reflect the finite tweezer width; the resulting interatomic distances then determine the 1/r^6 interaction strengths. This procedure follows the experimental protocols referenced in the paper and is a standard approximation in the Rydberg-array literature. While a direct, quantitative comparison with measured higher moments or spatial correlations from a specific experiment is not performed here, we have checked that the crossover to activated scaling and the localization of the floating phase remain robust across a range of disorder strengths. To address the referee's request we will expand the Methods section with a more explicit description of the disorder-generation algorithm, including its assumptions and a brief discussion of possible differences from real tweezer imperfections. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on direct numerical simulations

full rationale

The paper reports numerical studies of Kibble-Zurek dynamics and phase localization in a disordered Rydberg chain model. All central results (crossover to infinite-randomness scaling, localization of the floating phase while retaining the leading incommensurate wavevector) are obtained by direct computation of time evolution and correlation functions on finite chains with explicitly generated position disorder. No closed-form derivation, fitted parameter renamed as prediction, or self-citation chain is invoked to justify the outcomes; the disorder is introduced as an input model whose consequences are then measured. The work is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; no explicit free parameters, new entities, or ad-hoc axioms are stated.

axioms (1)
  • domain assumption Numerical methods can accurately capture the effects of quenched disorder on quantum phase transitions in one-dimensional spin chains.
    The study relies on this standard assumption for its numerical analysis of Kibble-Zurek dynamics and floating-phase localization.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Stabilization of bulk quantum orders in finite Rydberg atom arrays

    cond-mat.quant-gas 2026-04 unverdicted novelty 6.0

    A protocol leverages the disordered phase to set unbiased boundary configurations in finite Rydberg arrays, stabilizing bulk-like quantum order in 1D and 2D simulations.

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