Programmable glassy dynamics using tunable disorder in tweezer arrays

Grant W. Biedermann; Kaustav Mukherjee; Robert J. Lewis-Swan

REVIEW 4 major objections 4 minor 56 references

Programmable glassy dynamics using tunable disorder in tweezer arrays

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper establishes that the stretch exponent of glassy spin relaxation is governed by the spread of nearest-neighbor interaction strengths, through the scaling law $\beta = g(\Delta,d)\,J_0/\sigma_J$.

desk verdict A useful, mostly solid framework paper: the analytic sigma_J result and the beta vs J0/sigma_J collapse are real contributions, but the central scaling law is an empirical fit and the J-mapping is oversold in the abstract for small alpha. read the letter →

arxiv 2504.17659 v1 pith:QU54OYMZ submitted 2025-04-24 cond-mat.quant-gas cond-mat.dis-nnquant-ph

Kaustav Mukherjee , Grant W. Biedermann , Robert J. Lewis-Swan This is my paper · ORCID

classification cond-mat.quant-gascond-mat.dis-nnquant-ph

keywords glassydynamicsstretchedexponentialpositionaldisordertweezerarraysXXZmodelJ-mappingdipolarinteractionsquantumsimulation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that the slow, glassy relaxation of a disordered array of interacting quantum spins is controlled by a single statistical feature of the disorder: the spread (standard deviation) of nearest-neighbor interaction strengths. It proposes a scaling law, $\beta = g(\Delta,d)\,J_0/\sigma_J$, for the stretch exponent $\beta$ of the collective magnetization decay, and argues that $\sigma_J/J_0 \gtrsim 1$ is the condition for sub-exponential, glassy decay. It also introduces a construction called J-mapping, placing spins in a one-dimensional chain at separations $r_k = (J_0/J_k)^{1/\tilde{\alpha}}$, so that the chain reproduces the relaxation of dilute two- and three-dimensional disordered arrays. The practical payoff is a route to program slow, tunable relaxation in current tweezer-array quantum simulators of atoms and molecules, with possible uses in engineered quantum memories or batteries.

What carries the argument

The load-bearing object is the standard deviation $\sigma_J$ of the nearest-neighbor interaction distribution, together with the stretched-exponential ansatz $\langle \hat{S}_x \rangle = 0.5\exp[-(\gamma t)^\beta]$. The paper derives the analytic low-filling form $\sigma_J/J_0 = (\pi/\sqrt{6})\,\alpha/d$, then obtains the empirical scaling $\beta = g(\Delta,d)\,J_0/\sigma_J$ and shows that rescaling by $\sigma_J$ collapses simulation data for different $\alpha$. The second mechanism is the J-mapping construction $r_k = (J_0/J_k)^{1/\tilde{\alpha}}$, which converts a target interaction distribution into a deterministic one-dimensional chain; this is what lets a one-dimensional experiment emulate two- or three-dimensional disorder.

What would settle it

Compute or measure $\beta$ for two disorder distributions engineered to have the same $\sigma_J$ but different shapes, such as log-normal versus bimodal, at the same $d$ and $\Delta$; Eq. (4) predicts identical $\beta$. If the decay curves separate, the variance does not control the dynamics. The paper already flags the small-$\alpha$ regime ($\alpha \lesssim 2$) as the place to look, because next-nearest-neighbor contributions produce exactly such a separation.

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Extended reading notes

Core claim

The central claim is that the relaxation of the collective magnetization after a quench from a product state is characterized by a stretched exponential, and that the stretch exponent satisfies $\beta = g(\Delta,d)\,J_0/\sigma_J$, where $J_0$ sets the interaction scale and $\sigma_J$ is the standard deviation of the distribution of nearest-neighbor couplings. Because the analytic low-filling result gives $\sigma_J/J_0 = (\pi/\sqrt{6})\,\alpha/d$, the criterion $\sigma_J/J_0 \gtrsim 1$ translates directly into a prediction for when glassy ($\beta < 1$) dynamics occurs. The paper further claims that the variance of the disorder distribution, rather than its full shape, dimensionality, or interaction range, is the controlling parameter: rescaling $\beta$ by $\sigma_J$ collapses simulation data for XY, Ising, and XXZ models across $d = 1, 2, 3$. Finally, it claims that a one-dimensional array built by J-mapping, placing successive spins at $r_k = (J_0/J_k)^{1/\tilde{\alpha}}$ with $J_k$ sampled from the target disorder distribution, reproduces both the stretch exponents and the qualitative correlation dynamics of dilute 2D and 3D arrays, with known limitations when the power-law exponent is small ($\alpha \lesssim 2$), where next-nearest-neighbor interactions cannot be neglected.

Load-bearing premise

The argument rests on assuming that the full many-body relaxation dynamics is set by the variance of nearest-neighbor pair interactions; if interactions beyond nearest neighbors or correlated configurations contribute significantly, the scaling law loses its grip.

Editorial extensions

If this is right

Measured or engineered variance of nearest-neighbor couplings becomes a predictive handle: controlling $\sigma_J/J_0$ controls whether the decay is glassy and how slow it is.
A dilute 2D or 3D disordered array can be emulated in a one-dimensional tweezer chain by J-mapping, making higher-dimensional glassy dynamics accessible to 1D experiments for power-law exponents $\alpha \gtrsim 2$.
In a quasi-ordered one-dimensional array with transverse position disorder and dipolar interactions at the magic angle, $\beta$ can be tuned continuously from 2 down to about 0.4, that is, from fast relaxation to glassy behavior.
Correlation dynamics in the J-mapped array reproduce the short-time sub-ballistic spread proportional to $(J_0 t)^{1/3}$ and the long-time arrest with the same $1/\sqrt{f}$ scaling as dilute 2D arrays.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: if the variance-only scaling survives experiments, it suggests a practical calibration shortcut, namely measuring the interaction histogram rather than the full spatial configuration to predict relaxation.
Editorial inference: the framework invites a direct test with non-Poissonian correlated disorder; the authors list such disorder as future work, but the scaling would predict that $\beta$ tracks $\sigma_J$ even if higher-order correlations change.
Editorial inference: because the prefactor $g(\Delta,d)$ varies by only 15-20 percent across dimensions and anisotropies, the scaling may extend to other observables such as entanglement or correlation spreading, but that extension is not established here.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new things here are the analytic expression for sigma_J [Eq. (3)] and the data collapse of the stretch exponent beta against J0/sigma_J. The analytic derivation of sigma_J from the continuum nearest-neighbor distribution is clean and matches the numerics. The collapse across d = 1, 2, 3 and alpha = 2...6 for XY, Ising, and XXZ models is convincing, and the anchor to the known Ising pair-model result beta = d/alpha gives the scaling law more weight than a pure empirical fit would have. The J-mapping construction is a clever experimental design tool, and the validation against direct simulations, including the correlation propagation comparison, is a good-faith test. The authors also deserve credit for being upfront in the SM about where the mapping breaks down.

The soft spots are real but addressable. First, Eq. (4) is a fit, and the paper shows no error bars on the extracted beta or on g(delta, d), and no convergence checks with system size or disorder realizations. For a proposed universal relation, that is a gap, though not a fatal one. Second, the claim that the variance is a sufficient statistic for the disorder distribution is not tested against same-sigma, different-shape distributions. Without that control, Eq. (4) could be a coincidence of the specific distribution families simulated. Third, the abstract promises emulation for "arbitrary dimensionality and interaction range," but the paper itself shows the J-mapping with fixed tilde-alpha = 3 fails for alpha <~ 3, and only works across the full range when tilde-alpha is matched to alpha. The wording should be softened to reflect the demonstrated regime. Fourth, the N = 8 system size is small, and while the dilute limit plus disorder averaging helps, it would be better to see at least a few checks at larger N, even with semiclassical methods. The partial circularity of extracting g from the same class of data used to predict beta is mitigated by the Ising anchor but should be acknowledged more explicitly.

Overall, I think this is a valuable paper for the tweezer quantum simulator community. The analytic sigma_J result alone is worth publishing, and the scaling framework is plausible and well-supported within its tested regime. The issues are matters of evidence and framing, not load-bearing flaws. It deserves a serious referee and, after moderate revision, publication.

Referee Report

4 major / 4 minor

Summary. The manuscript proposes that the stretched-exponential relaxation of the collective magnetization in positionally disordered spin ensembles is governed by the standard deviation sigma_J of the nearest-neighbor interaction distribution, expressed as beta = g(Delta,d) J0/sigma_J in Eq. (4). The authors derive analytically the f -> 0 scaling sigma_J/J0 = (pi/sqrt(6))(alpha/d) in the Supplemental Material, show numerical scaling collapse across XY, Ising, and XXZ models in d = 1, 2, 3 dimensions, and introduce a J-mapping method that constructs bespoke 1D arrays whose nearest-neighbor interaction distribution replicates that of dilute 2D or 3D systems. They validate the mapping for stretch exponents and correlation dynamics, and demonstrate tunable glassy relaxation in quasi-ordered 1D arrays using anisotropic dipolar interactions.

Significance. If the proposed scaling law holds, it gives a useful design rule: glassy relaxation requires sigma_J/J0 of order unity or larger, and one can emulate higher-dimensional disordered systems in experimentally accessible 1D tweezer arrays. The strengths of the paper are the clean analytic derivation of the variance in the Supplemental Material, the broad numerical coverage (alpha = 2 through 6, Delta = 0, 0.6, and Ising, d = 1 through 3), and a concrete, experimentally relevant proposal for programmable disorder. However, the central claim that the variance is a sufficient statistic for the disorder distribution is supported only by exact-diagonalization fits at N = 8 with no quoted uncertainties, and the abstract's promise of emulation for arbitrary dimensionality and interaction range goes beyond what is demonstrated in the body of the paper.

major comments (4)

[Role of disorder statistics; Eq. (4); Fig. 2(a-c)] The central scaling beta = g(Delta,d) J0/sigma_J is established by fitting stretched exponentials to exact-diagonalization data at N = 8 and filling fraction f = 0.01, yet the paper reports no error bars, no number of disorder realizations, no fit ranges, and no system-size convergence checks. Because g is read off from the same fits as beta, the collapse in Fig. 2(d-f) is largely a consistency check of the fitting procedure rather than an independent verification of Eq. (4). The log-normal and quasi-ordered tests are independent and helpful, but they inherit the same fitting uncertainties. Please provide uncertainties on beta and g, a finite-N study, or an explicit statement of the precision of the empirical law.
[Eq. (4) and J-mapping; Fig. 2 and Fig. 3] The assertion that sigma_J fundamentally governs beta is not distinguished from distribution-shape dependence. All simulated distributions belong to the same family (nearest-neighbor spacings of dilute arrays, or log-normal), so a control with two different P(J) families having identical sigma_J (for example, log-normal versus bimodal) is needed. Without such a control, Eq. (4) cannot exclude the possibility that higher cumulants or the functional form of P(J) control beta and that sigma_J merely correlates with them. This is load-bearing because the J-mapping method intentionally reproduces only sigma_J and the mean of the interaction distribution.
[Abstract and section 'Tunable relaxation in 1D arrays'; Fig. 3(b); SM Fig. 6 and SM Fig. 7] The abstract claims emulation of disordered systems with arbitrary dimensionality and interaction range, but J-mapping with fixed tilde{alpha} = 3 fails for alpha <~ 2, as shown in Fig. 3(b), and SM Fig. 7 shows that the next-nearest-neighbor distributions of the 2D array and the J-mapped chain diverge in exactly that regime. The authors acknowledge this and SM Fig. 6(a) shows that choosing tilde{alpha} = alpha repairs the mismatch for the 2D case, but the analogous tilde{alpha} = alpha test for the 3D case is not shown. Please either demonstrate the mapping for 3D with tilde{alpha} = alpha and quantify the residual discrepancy, or qualify the claim to the regime where the mapping is actually validated.
[Supplemental Material, Eqs. (9)-(15); Fig. 1(c)] The analytic result sigma_J/J0 = (pi/sqrt(6))(alpha/d) is derived from a continuous Poisson ansatz valid in the f -> 0 limit, while Fig. 1(c) shows that sigma_J decreases with increasing f, and the numerical analysis in Fig. 2 is carried out at f = 0.01, outside the regime f <~ 1e-3 where Eq. (3) is validated. Since the g values in Table I are extracted at f = 0.01 and carry no uncertainties, the finite-filling scatter could be comparable to the claimed dependence on dimension and anisotropy. Please quantify the systematic error due to f = 0.01, for example by reporting g at a smaller f or by estimating the f-correction to Eq. (3).

minor comments (4)

[After Eq. (5)] The text says 'Figure 2 (a-c) shows the variation of the extracted beta with 1/sigma_J' for the log-normal distribution; the correct reference appears to be Fig. 3, since Fig. 2 shows dilute-array results.
[Caption of Fig. 4(b)] The blue line is labeled as 'predicted g(Delta,d)/sigma_J', but Eq. (4) predicts beta = g(Delta,d) J0/sigma_J, so given the horizontal axis J0/sigma_J the line should be labeled g(Delta,d) J0/sigma_J.
[SM Table I] The g(Delta,d) values are quoted to six significant figures without uncertainties, which is inconsistent with the 15-20% scatter discussed in the text; reporting fewer digits or adding error bars would be more appropriate.
[Methods and numerics] The manuscript does not state the number of disorder realizations, the time range used for the stretched-exponential fit, or the fitting procedure for extracting beta; adding a short methods paragraph would make the numerical claims reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (4) is an empirical scaling law whose prefactor is fitted to dilute-array data, but its later use for J-mapped, log-normal, and quasi-ordered arrays is an out-of-sample test rather than a forced identity, and the Ising limit is anchored to the analytic pair-model result.

full rationale

The paper's central relation, beta = g(Delta,d) J0/sigma_J, is explicitly introduced as an empirical expression (“This leads us to propose an empirical expression”), with g(Delta,d) read off from slopes of beta versus J0/sigma_J in Fig. 2. That procedure is a fit, not a derivation, but it is not circular: the scaling is then checked against independent simulations of J-mapped log-normal chains, J-mapped emulations of 2D and 3D dilute arrays, and quasi-ordered arrays. In each of those cases, the beta values are obtained by direct time evolution, not by insertion into Eq. (4), so agreement is a genuine out-of-sample test. In particular, Fig. 4(b) uses g(0,1) from Table I (fitted to dilute 1D XY data) as a predicted line for a quasi-ordered geometry; this is a predictive extrapolation, and the simulated quasi-ordered points could have disagreed. The Ising limit is separately anchored to the known pair-model result beta_pair = d/alpha, which, combined with the analytic sigma_J ∝ alpha/d scaling of Eq. (3), gives g ≈ pi/sqrt(6), consistent with the tabulated Ising values. The self-citation to Ref. [52] supplies supporting distribution formulas and scaling facts, but the central collapse and emulation claims do not reduce to that citation. The acknowledged failure for alpha ≲ 2, where next-nearest-neighbor interactions matter and the N-NN distributions diverge (SM Fig. 7), is a limitation of the variance-only hypothesis, not a circularity. No equation is defined in terms of the quantity it is claimed to predict, and no fitted parameter is renamed as an independent first-principles prediction.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The framework introduces no new physical entities. The main theoretical input beyond the Hamiltonian is the empirical prefactor g(delta,d), fitted to the numerical data. The Poisson-neighbor assumption and the stretched-exponential ansatz are the key domain assumptions.

free parameters (1)

g(delta,d) = Table I: 1.05152-1.29921 (1D-3D, delta = 0, 0.6, Ising)
The prefactor in Eq. (4) is obtained from linear fits to the beta versus J0/sigma_J data in Fig. 2(a-c). It is a function of anisotropy delta and dimension d, not derived from first principles.

assumptions (4)

domain assumption Nearest-neighbor spacing in dilute arrays follows the Poisson-based distributions P1D, P2D, P3D of Eqs. (6)-(8).
Assumes uncorrelated random placement of atoms with filling fraction f, used to derive Eq. (3) in the SM.
domain assumption Collective magnetization relaxation is well described by a stretched exponential <Sx> = 0.5 exp[-(gamma t)^beta].
This functional form is assumed throughout; beta and gamma are then extracted from numerical time traces. The paper does not test alternatives.
domain assumption In the dilute limit the dynamics is governed by independent pairs of strongly interacting spins (pair/cluster model).
Used to motivate the relevance of the nearest-neighbor interaction distribution and to derive the pair-model prediction beta = d/alpha.
domain assumption Exact numerical integration with N=8 qubits and many disorder realizations converges to the thermodynamic limit via self-averaging.
The paper asserts this convergence without showing explicit checks in system size or number of disorder realizations.

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Pith. "Pith review of Programmable glassy dynamics using tunable disorder in tweezer arrays." pith.science (2026). https://pith.science/paper/QU54OYMZ

@misc{pith2026250417659,
  author       = {Pith},
  title        = {Pith review of: Programmable glassy dynamics using tunable disorder in tweezer arrays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QU54OYMZ}},
  note         = {Machine review of arXiv:2504.17659}
}

read the original abstract

We propose a unifying framework for non-equilibrium relaxation dynamics in ensembles of positionally disordered interacting quantum spins based on the statistical properties, such as mean and variance, of the underlying disorder distribution. Our framework is validated through extensive exact numerical calculations and we use it to disentangle and understand the importance of dimensionality and interaction range for the observation of glassy (i.e., sub-exponential) decay dynamics. Leveraging the deterministic control of qubit positioning enabled by modern tweezer array architectures, we also introduce a method (``J-mapping'') that can be used to emulate the relaxation dynamics of a disordered system with arbitrary dimensionality and interaction range in bespoke one-dimensional arrays. Our approach paves the way towards tunable relaxation dynamics that can be explored in quantum simulators based on arrays of neutral atoms and molecules.

Figures

Figures reproduced from arXiv: 2504.17659 by the authors.

**Figure 2.** (a-c). In all cases, we observe the stretch exponent is inversely proportional to the standard deviation of distribution i.e. β ∝ 1/σJ in the regime of J0/σJ < 1, with minor variations in slopes depending on d and ∆. This leads us to propose an empirical expression for the stretch exponent of the form β = g(∆, d)J0/σJ . (4) This leads to two key arguments that both align with and extend beyond the pair model predic… view at source ↗

**Figure 4.** FIG. 4. (a) Variation of the stretch exponent [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: FIG. 5. Variation in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. (a) Variation of stretch exponent [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7. Next-nearest neighbor (N-NN) distribution for [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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