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Stability of many-body localization in two dimensions

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper reports that in two dimensions, random disorder lets rare thermal regions destabilize many-body localization as system size grows, while quasiperiodic disorder shows no such size dependence and may keep MBL stable.

desk verdict Strong, careful experiment with a genuinely new finite-size scaling comparison, but the quasiperiodic stability claim is not established: the flat Wc(L) is exactly what a pre-avalanche regime predicts, and the paper never checks time dependence for QP. read the letter →

arxiv 2508.20699 v1 pith:FI4SKM4F submitted 2025-08-28 cond-mat.quant-gas cond-mat.dis-nncond-mat.stat-mech

Junhyeok Hur , Joey Li , Byungjin Lee , Kiryang Kwon , Minseok Kim , Samgyu Hwang , Sumin Kim , Yong Soo Yu
show 3 more authors
Amos Chan Thorsten Wahl Jae-yoon Choi
This is my paper · ORCID
classification cond-mat.quant-gascond-mat.dis-nncond-mat.stat-mech
keywords many-bodylocalizationtwodimensionsavalancheinstabilityquasiperiodicdisorderrandomultracoldatomsopticallatticeimbalance
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

The paper tests whether many-body localization (MBL) — the failure of a strongly disordered interacting quantum system to thermalize — can survive in two dimensions. It compares two disorder types in the same ultracold-atom platform: uncorrelated random disorder, where rare weakly disordered regions can seed thermal avalanches, and quasiperiodic disorder, which lacks such rare regions. Measuring the imbalance after 1500 tunneling times on systems from 8×8 to 24×24 sites, the authors find that the random-disorder crossover shifts to higher disorder strength as system size grows, matching the avalanche prediction, while the quasiperiodic crossover is flat in system size. They conclude that two-dimensional MBL is fragile under random disorder but may be stable under quasiperiodic disorder.

What carries the argument

The load-bearing observable is the imbalance I = (n_odd - n_even)/(n_odd + n_even), which measures memory of a stripe initial state. The crossover point Wc(L) is extracted by fitting imbalance-vs-disorder curves with an empirical function I_s(W) = a(W - Wc)^(2/3) + b; the system-size dependence of Wc(L) then separates a stable phase (Wc converging) from an unstable one (Wc diverging). The disorder potentials are programmed with a digital micromirror device, giving uncorrelated random disorder and a quasiperiodic potential with incommensurate frequencies.

What would settle it

Measure the quasiperiodic crossover on a larger system (e.g., 32×32) at hold times longer than 1500 tunneling times and check whether Wc,q drifts upward with L or t. Avalanche theory predicts Wc(t) ~ exp[c(ln ln t)^(1/3)] and a size drift once t exceeds tdeloc(L) ~ exp(const·L); a flat Wc,q under both larger L and longer t would support stability, while an upward drift would falsify it. Alternatively, engineer a single weakly disordered bubble and track its growth: avalanche theory predicts the melted region expands exponentially in time, whereas quasiperiodic stability predicts it stays compa

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Extended reading notes

Core claim

On a single quantum-gas-microscope platform, the authors trace the thermal-to-MBL crossover in two dimensions for two disorder potentials. The central quantitative finding is the scaling of the extracted crossover disorder Wc(L): for uniform random disorder, Wc shifts upward with increasing system size and follows the avalanche asymptotic form Wc(L) ~ exp(c ln^(1/3) L^2), while for quasiperiodic disorder, Wc stays constant across L = 8 to 24. The authors interpret this as evidence that rare thermal bubbles in random disorder grow, merge, and eventually restore ergodicity, whereas quasiperiodicity suppresses such rare regions, allowing MBL to remain stable in the accessible regime.

Load-bearing premise

The observation window of 1500 tunneling times is long enough that the flat size-dependence of the quasiperiodic crossover reflects long-time stability rather than a pre-avalanche transient that would also look flat.

Editorial extensions

If this is right

  • For uncorrelated random disorder, two-dimensional MBL is not a stable phase in the thermodynamic limit: Wc(L) grows with L along the avalanche curve, so the localized regime is expected to thermalize at sufficiently large scales.
  • For quasiperiodic disorder, the crossover stays at constant Wc across system sizes up to 24×24, consistent with a genuine MBL phase in two dimensions rather than a transient.
  • The avalanche mechanism's time signature is confirmed: at short hold times the random-disorder crossover is nearly size-independent, while at long hold times the size dependence emerges only for random disorder.
  • The platform enables systematic finite-size scaling in 2D, opening a route to quantitative studies of critical behavior at the quasiperiodic ergodic-to-MBL transition.
  • Avalanche theory still allows a much longer delocalization time for quasiperiodic systems, so the reported stability is established within the experimental time window regardless of the thermodynamic limit.

Reading between the lines

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

  • If the flat quasiperiodic crossover persists at larger sizes and longer times, the quasiperiodic MBL transition in 2D likely belongs to a different universality class from the random-disorder transition; measuring critical exponents near Wc,q would distinguish the scenarios.
  • Because avalanche theory predicts Wc(t) ~ exp[c(ln ln t)^(1/3)] even for an unstable system, the flat quasiperiodic curve could be mimicked by a pre-avalanche transient with t < tdeloc(L); a direct bound on the delocalization time would settle this ambiguity.
  • An engineered single thermal bubble placed in a quasiperiodic background should remain compact, whereas the same bubble in random disorder should expand; this is a testable extension the paper gestures toward.
  • The rare-region argument sharpens in three dimensions: random disorder should be even more fragile and quasiperiodic disorder possibly still stable, so extending the comparison to 3D would test the disorder-dependent scenario.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This manuscript reports a cold-atom quantum simulation experiment studying the stability of many-body localization (MBL) in two dimensions. Using a single-site-resolved disordered Bose-Hubbard system with system sizes from 8×8 to 24×24 and evolution times up to 1500 tunneling times, the authors measure the imbalance as a function of disorder strength for two disorder types: uniform random and quasiperiodic. Extracting a crossover disorder Wc(L) from an empirical fit, they find that for random disorder Wc increases with L, which they interpret as consistent with the avalanche instability scenario; for quasiperiodic disorder Wc is approximately L-independent, interpreted as evidence that quasiperiodic disorder suppresses avalanches and may stabilize 2D MBL. Numerical TDVP simulations for L=6,8 are reported as complementary evidence.

Significance. If substantiated, the disorder-type contrast would be an important experimental step in the 2D MBL debate, directly testing rare-region avalanche theories and reaching system sizes and times beyond exact numerics. The platform's strengths include controlled generation of two disorder classes, finite-size scaling to 576 sites, a time-dependence check for random disorder, and an independent numerical complement. However, the central positive claim is conditional: the flat Wc,q(L) is also the pre-avalanche signature of an unstable system within the authors' own framework, so the data as presented support 'possible stability' (the abstract's wording) rather than the stronger conclusion that quasiperiodic MBL 'remains stable'.

major comments (4)
  1. [Quantum avalanche with time; System size scaling] The flat Wc,q(L) in Fig. 3(c) is precisely what the paper's own avalanche discussion predicts when t < tdeloc(L) for all L: Wc then depends on t, not on L. The time-dependence check (Fig. 4) is performed only for random disorder; no analogous measurement or bound on tdeloc,q(L) is given for quasiperiodic disorder. Given the conceded limitation ('we might not be able to discern the true localization within our experimental time window'), the data do not distinguish stable MBL from a slow QP avalanche with tdeloc,q(L) >> 1500τ. The abstract's 'suggesting possible stability' is supported; the conclusion's 'remains stable' is not. A QP t=150τ vs 1500τ scan, or an explicit quantitative bound, is needed.
  2. [System size scaling (empirical fit)] All Wc(L) values come from Is(W)=a(W−Wc)^{2/3}+b. The 2/3 exponent is presented as empirical, and no robustness test is reported. Wc and its 1σ error bars are conditional on this functional form; a different choice (e.g., linear, free exponent p, or excluding the plateau) could alter the apparent L-dependence, especially for quasiperiodic disorder where the transition is shallow. Please justify the exponent or show explicitly that the flat-vs-increasing contrast survives alternative fits.
  3. [System size scaling, Fig. 3(c)] The comparison with avalanche theory is visual. The plotted asymptotic curve W_c^th(L) ∼ exp(c1 ln^{1/3}L^2) is not quantitatively assessed (no fit, no residuals, no comparison to the null hypothesis of constant Wc), and the theory is asymptotic while the data are at 8≤L≤24. The claim 'consistent with the avalanche scenario' should be either quantified or stated more weakly.
  4. [Introduction / Fig. 1(e)] The claim that quasiperiodic disorder suppresses rare regions is asserted without a quantitative finite-size statement. For the two-cosine potential with random phases, low-disorder patches are deterministic and will occur somewhere in any finite L×L window; their areal density, depth, and possible connectivity should be characterized (e.g., via the distribution of local potential minima) to support the argument that they cannot seed an avalanche within the experimental window. Without this, the 'avalanche-suppressed' interpretation is not uniquely constrained by the data.
minor comments (5)
  1. [Breakdown of thermalization] The text quotes Wr=147 J and Wq=61 J, while Fig. 2 and its insets appear to use Wr=0,30,61 and Wq=0,70,140; please reconcile the labels/values.
  2. [Fig. 3 caption] 'A global offsets of 0.15' should read 'A global offset of 0.15'; please also specify whether the offset is added to all but one curve and whether error bars are shifted with the data.
  3. [Supplemental, Fig. S7 caption / text] 'quasiperiodic random disorder' in the Fig. S7 caption is a typo; it should read 'quasiperiodic disorder'. The main text also alternates between 'quasi-periodic' and 'quasiperiodic'; please standardize.
  4. [Supplemental II, Numerical simulations] The transition point for QP is defined by where the decay exponent b first reaches zero, but the text states that the I(t)=At^{-b} fit is 'not reliable' in the MBL regime. Please describe this criterion more concretely and show the sensitivity of Wc,q to the fitting window (t≥70) and to the identification of b=0.
  5. [General] No data/code availability statement is included. Given the large experimental dataset and the arXiv posting, a data availability statement would improve reproducibility.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the experimental finite-size study is self-contained; only minor, non-load-bearing self-citations are present.

full rationale

The paper's central inference is an experimental measurement: imbalance at t=1500τ for system sizes L=8 to 24 under random and quasiperiodic disorder, with the crossover Wc(L) extracted from an explicitly empirical fit I_s(W)=a(W−Wc)^{2/3}+b. The avalanche comparison uses the theoretical curve W_th_c,r(L)∼exp[c1 ln^{1/3} L^2] with c1 taken from Refs [24,32]—external results, not fitted to the data—and the quasiperiodic constant line is only a guide to the eye. The numerical simulations in the Supplemental Material are new TDVP calculations following Ref [32] and implemented with TeNPy; they are not prior fitted parameters renamed as predictions. Self-citations (Refs [33,34,46,53,57]) concern numerical techniques and DMD calibration, and they do not carry the stability conclusion. The paper explicitly concedes the finite-time limitation: 'we might not be able to discern the true localization within our experimental time window.' Thus the quasiperiodic stability claim is vulnerable to the unexcluded pre-avalanche alternative (t_deloc,q(L) >> 1500τ), but that is an interpretive weakness, not a definitional or statistical circularity. No equation in the paper reduces the predicted quantity to a fitted input. Score 2 reflects only the presence of minor, non-load-bearing self-citations.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a finite-time observable and an empirical fit, plus the accepted avalanche framework. No new entities are postulated. The largest untested inputs are the fit form and the sufficiency of the observation window.

free parameters (3)
  • Exponent p in empirical transition curve I_s(W)=a(W-W_c)^p+b = 2/3
    Chosen ad hoc to fit the imbalance-vs-disorder curves; this exponent determines W_c and thus the size scaling that is the central result.
  • Fit coefficients a and b for each system size and disorder type = fitted per curve
    Free parameters of the empirical fit; not derived from theory.
  • Power-law fit exponent b in numerical I(t)=A t^{-b} = fitted
    Used to extract numerical W_c values for L=6 and L=8.
assumptions (4)
  • domain assumption The finite-time imbalance at t=1500 tau is a faithful indicator of the MBL regime, and the system size dependence of the fitted crossover reflects the asymptotic phase structure.
    The paper itself acknowledges that the relaxation time scale can exceed the experimental window (Section 'BREAKDOWN OF THERMALIZATION'), so this is a necessary assumption for interpreting Wc(L) as stability information.
  • ad hoc to paper The empirical functional form I_s(W)=a(W-W_c)^{2/3}+b captures the crossover shape, and W_c is a meaningful crossover point.
    The 2/3 exponent is not derived; it is chosen to describe the observed transition curves.
  • domain assumption The avalanche theory of Refs [23,24] and its extension in Ref [32] correctly predicts the asymptotic scaling W_c(L) ~ exp(c1 ln^{1/3} L^2).
    The paper uses this theoretical curve as a benchmark for the random-disorder data; it is not independently derived in this work.
  • domain assumption Heating is negligible over the 1500 tau hold time so the dynamics are effectively isolated.
    Supplemental Fig. S6 gives a heating rate dT/dt=0.8 U/s, which over ~2.8 s corresponds to a temperature increase of ~2.3 U, comparable to U; the paper does not quantify the effect of this heating on the imbalance.

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Pith. "Pith review of Stability of many-body localization in two dimensions." pith.science (2026). https://pith.science/paper/FI4SKM4F

@misc{pith2026250820699,
  author       = {Pith},
  title        = {Pith review of: Stability of many-body localization in two dimensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FI4SKM4F}},
  note         = {Machine review of arXiv:2508.20699}
}
abstract

Disordered quantum many-body systems pose one of the central challenges in condensed matter physics and quantum information science, as their dynamics are generally intractable for classical computation. Many-body localization (MBL), hypothesized to evade thermalization indefinitely under strong disorder, exemplifies this difficulty. Here, we study the stability of MBL in two dimensions using ultracold atoms in optical lattices with variable system sizes up to $24\times 24$ sites, well beyond the classically simulable regime. Using the imbalance as a probe, we trace the long-time dynamics under two distinctive disorder potentials: quasiperiodic and random disorder. For random disorder, the MBL crossover point shifts to higher disorder strength with increasing system size, consistent with the avalanche scenario. In contrast, with quasiperiodic disorder, we observe no clear system size dependence, suggesting possible stability of MBL in two dimensions.

Figures

Figures reproduced from arXiv: 2508.20699 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. displays the time evolution of the imbalance [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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