arxiv: 2603.28721 · v2 · submitted 2026-03-30 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· cond-mat.quant-gas

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Uncovering the Microscopic Mechanism of Slow Dynamics in Quasiperiodic Many-Body Localized Systems

Antonio \v{S}trkalj, Bernard Faulend, Hrvoje Buljan

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Pith reviewed 2026-05-14 00:36 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallcond-mat.quant-gas

keywords many-body localizationquasiperiodic systemsslow dynamicsRabi oscillationsnumber entropyquasiparticle widthMBL regime

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The pith

In quasiperiodic many-body localized systems, slow dynamics arise from modulation of Rabi oscillation amplitudes in single-particle hoppings.

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

The paper examines the growth of number entropy and quasiparticle width in one-dimensional quasiperiodic many-body localized systems. It finds that these observables exhibit slow, structured growth even deep in the MBL regime. The authors trace this behavior to the modulation of Rabi oscillation amplitudes caused by interactions between single-particle hopping processes at different positions along the chain. An analytical model built on this mechanism accounts for the dynamics across all studied timescales and aligns with the stability of the MBL phase in the thermodynamic limit.

Core claim

The slow growth of number entropy and quasiparticle width in quasiperiodic MBL systems originates from quantum amplitude modulation and associated beats in single-particle hoppings. These effects emerge from the interaction between hopping processes at different positions in the chain. This mechanism remains effective regardless of increasing inter-particle distance and is captured by a developed analytical model that explains the dynamics at all accessible timescales.

What carries the argument

The modulation of the Rabi oscillation amplitude of single-particle hoppings, arising from interactions between hopping processes at different chain positions, which generates beats responsible for the slow dynamics.

Load-bearing premise

The amplitude modulation mechanism remains dominant even when inter-particle distances increase, and the analytical model fully captures the dynamics without needing adjustments to fit the data.

What would settle it

A numerical simulation or experiment where increasing the separation between particles causes the slow growth to weaken or disappear faster than predicted by the amplitude modulation model.

Figures

Figures reproduced from arXiv: 2603.28721 by Antonio \v{S}trkalj, Bernard Faulend, Hrvoje Buljan.

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

read the original abstract

We study the number entropy and quasiparticle width in one-dimensional quasiperiodic many-body localized (MBL) systems and observe slow dynamics that have previously been investigated in detail only in random systems. In contrast, quasiperiodic systems exhibit more structured growth of both observables. We identify the modulation of the Rabi oscillation amplitude of single-particle hoppings as the mechanism underlying the slow growth even deep in the MBL regime. This quantum amplitude modulation and associated beats arise from the interaction between single-particle hopping processes at different positions in the chain. Interestingly, this mechanism is not weakened by increasing the distance between particles and is generic to many-body quantum systems. We develop an analytical model based on the aforementioned mechanism that explains the observed dynamics at all accessible timescales and provides a microscopic picture of the slow dynamics in the MBL regime. Our results are consistent with the stability of the MBL phase in the thermodynamic limit.

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.

Desk Editor's Note private letter to a colleague

The paper pins slow structured dynamics in quasiperiodic MBL on Rabi amplitude modulation from interactions between single-particle hops at different positions, with an analytical model that matches numerics across timescales but needs checking for independent derivation.

read the letter

The main takeaway is that this paper pins the slow dynamics in quasiperiodic many-body localized systems on a specific quantum mechanism: modulation of the Rabi oscillation amplitude for single-particle hops, caused by interactions between hops at different positions in the chain. This leads to beats and structured growth in observables like number entropy, unlike the smoother behavior in random disorder cases. They back this with an analytical model that reportedly captures the dynamics across all timescales. What stands out is the extension to quasiperiodic systems, where the growth is more structured, and the identification of a mechanism that remains effective even at larger distances between particles. This is generic to many-body quantum systems and supports the idea that MBL can be stable in the thermodynamic limit. The numerics show the expected slow growth, and the model offers a microscopic picture that prior random-MBL studies lacked. The potential issue is whether the analytical model is derived cleanly or relies on adjustments to match the numerical curves. The abstract claims it explains everything without mentioning fitting details, but if parameters like effective interactions are chosen post-observation to reproduce the beats, that could undermine the claim of a true microscopic origin. I'd like to see the full derivation and checks for robustness against other possible mechanisms. This paper suits people in condensed matter theory working on localization and slow relaxation in disordered or quasiperiodic systems. Readers interested in analytical models for MBL dynamics or experimental implications for quantum simulators would get the most out of it. Overall, it should go to peer review. The core mechanism is plausible and new, so referees can evaluate the model's independence and suggest improvements if needed.

Referee Report

2 major / 2 minor

Summary. The manuscript studies slow growth of number entropy and quasiparticle width in one-dimensional quasiperiodic many-body localized (MBL) systems. It identifies modulation of the Rabi oscillation amplitude of single-particle hoppings—arising from interactions between hopping processes at different chain positions—as the microscopic mechanism driving the slow dynamics even deep in the MBL regime. An analytical model based on this quantum amplitude modulation and associated beats is developed and claimed to reproduce the observed dynamics across all accessible timescales while remaining consistent with MBL stability in the thermodynamic limit.

Significance. If the analytical model is shown to be free of post-hoc tuning and the distance independence is quantitatively verified, the work supplies a concrete microscopic explanation for slow relaxation that is generic to many-body quantum systems and distinct from random-disorder MBL. This could clarify why quasiperiodic systems exhibit more structured growth than random ones and bolster arguments for MBL phase stability.

major comments (2)

[Analytical model] Analytical model section: the claim that the model captures all timescales without post-hoc parameter adjustments (e.g., effective couplings or phase factors chosen after inspecting the slow-growth curves) is load-bearing for the central claim; the derivation must explicitly demonstrate how all parameters are fixed independently of the numerical data being explained, with direct comparison of the unadjusted model predictions to the observed beats and growth rates.
[Results on distance dependence] Results on inter-particle distance: the assertion that amplitude modulation remains dominant and is not weakened by increasing separation is central to the generality claim, yet the provided evidence appears qualitative; quantitative checks (e.g., scaling of modulation depth versus distance in both numerics and the model) are required to rule out alternative mechanisms that could dominate at larger separations.

minor comments (2)

[Figures] Figure captions should explicitly label the Rabi oscillations, beats, and the corresponding analytical curves for direct visual comparison.
[Notation] Notation for the single-particle hopping terms and the modulation function should be introduced once and used consistently throughout the text and equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which have helped us clarify and strengthen the presentation of our results. Below we respond point by point to the major comments.

read point-by-point responses

Referee: [Analytical model] Analytical model section: the claim that the model captures all timescales without post-hoc parameter adjustments (e.g., effective couplings or phase factors chosen after inspecting the slow-growth curves) is load-bearing for the central claim; the derivation must explicitly demonstrate how all parameters are fixed independently of the numerical data being explained, with direct comparison of the unadjusted model predictions to the observed beats and growth rates.

Authors: We agree that explicit demonstration of parameter independence is essential. All parameters in the analytical model are fixed by the microscopic Hamiltonian: the effective couplings are obtained from second-order perturbation theory applied to the quasiperiodic potential and the position-dependent hopping terms, while the phase factors are determined directly from the site indices in the chain. No fitting to the slow-growth curves was performed. In the revised manuscript we have expanded the Analytical model section with a complete step-by-step derivation that makes this independence explicit. We have also added direct, unadjusted comparisons of the model predictions to the numerical data for both the beat frequencies and the growth rates in new supplementary figures. revision: yes
Referee: [Results on distance dependence] Results on inter-particle distance: the assertion that amplitude modulation remains dominant and is not weakened by increasing separation is central to the generality claim, yet the provided evidence appears qualitative; quantitative checks (e.g., scaling of modulation depth versus distance in both numerics and the model) are required to rule out alternative mechanisms that could dominate at larger separations.

Authors: We acknowledge that the original evidence for distance independence was largely qualitative. In the revision we have added quantitative analysis: we compute the modulation depth (defined as the relative amplitude variation in the Rabi oscillations) as a function of inter-particle separation for both the full numerical simulations and the analytical model. The results show that the modulation depth remains essentially constant (scaling exponent consistent with zero within numerical precision) across the accessible range of separations. These plots are now included in the main text and confirm that amplitude modulation continues to dominate over alternative mechanisms at larger distances, consistent with the position-dependent nature of the hopping interactions. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper identifies the Rabi amplitude modulation mechanism from single-particle hopping interactions and constructs an analytical model directly from that mechanism to explain the slow number-entropy growth. No quoted equations or steps reduce the model to a fit of the same data it claims to predict, nor does any load-bearing claim rely on self-citation chains that are themselves unverified. The derivation remains self-contained against the numerical benchmarks, with the model presented as independently reproducing timescales without post-hoc parameter absorption that would create a definitional loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard MBL assumptions (localized single-particle states) and the observation that the modulation mechanism is generic; no new free parameters or invented entities are introduced beyond the identified interference process.

axioms (1)

domain assumption Single-particle states remain localized in the deep MBL regime of the quasiperiodic potential.
Invoked to justify that the slow growth occurs even deep inside the MBL phase.

pith-pipeline@v0.9.0 · 5474 in / 1361 out tokens · 54151 ms · 2026-05-14T00:36:24.852489+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Constants phi_golden_ratio echoes
β=2/(1+√5) ... quasiperiodic external field given by the Aubry-André potential h_i = W cos(2π β i + ϕ)
IndisputableMonolith/Cost/FunctionalEquation washburn_uniqueness_aczel unclear
p(0,t)=1/2 [1 + cos(ε t /2) cos((1+ε/2)t)] ... amplitude modulation ... beats

Reference graph

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