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arxiv: 2606.02207 · v1 · pith:TIZS2UKUnew · submitted 2026-06-01 · 🪐 quant-ph · cond-mat.dis-nn· hep-th

Information scrambling in all-to-all interacting models

Abhik Kumar Saha , Tanay Pathak , Masaki Tezuka This is my paper

Pith reviewed 2026-06-28 14:09 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.dis-nnhep-th
keywords information scramblingSYK modelentanglement entropyentanglement negativityquantum chaosall-to-all interactionsRényi entropy
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The pith

Von Neumann and Rényi entropies saturate near Haar-random values in all-to-all spin SYK models, signaling efficient scrambling.

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

The paper studies information scrambling in all-to-all interacting spin models that generalize the SYK model to multi-body interactions. It tracks the process with both standard entanglement entropies and mixed-state measures such as negativity. The entropies rise quickly and then level off close to the values expected for completely random quantum states. A numerical relation appears between one form of mutual information and negativity when the interaction is simplest, and negativity itself traces a Page-curve pattern when the two subsystems are sized differently. These patterns together give a description of how information spreads in systems where every spin couples to all others.

Core claim

In the all-to-all interacting spin SYK-q model, von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations.

What carries the argument

The all-to-all interacting spin SYK-q model probed through von-Neumann, Rényi, and mixed-state entanglement measures.

Load-bearing premise

Numerical results obtained on finite system sizes and chosen Hamiltonian scalings represent the thermodynamic limit without dominant finite-size artifacts.

What would settle it

A direct computation on significantly larger systems showing that saturation values remain far below Haar-random predictions or that the reported universal relation between Rényi-1/2 mutual information and negativity fails to appear for the minimal interaction order.

Figures

Figures reproduced from arXiv: 2606.02207 by Abhik Kumar Saha, Masaki Tezuka, Tanay Pathak.

Figure 1
Figure 1. Figure 1: FIG. 1. Evolution of (a) the average von-Neumann EE and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The dynamics of the average von-Neumann EE for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The dynamics of the average ( [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. The dynamics of the average von-Neumann EE for the spin SYK model with [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The dynamics of average von-Neumann EE for the usual SYK model with [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Dynamics of the average von-Neumann entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dynamics of the average von-Neumann entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Dynamics of the average von-Neumann entanglement entropy [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Dynamics of the average von-Neumann EE (upper panel) and 2-RE for spin SYK- [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Dynamics of the average von-Neumann EE (upper panel) and 2-RE for spin SYK- [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Dynamics of the average von-Neumann EE (upper panel) and 2-RE for spin SYK- [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The dynamics of Rényi-1/2 mutual information [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The dynamics of Rényi-1/2 mutual information [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The dynamics of the average von-Neumann EE for different values of [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Evolution of (a) average von-Neumann EE and (b) 2-RE with time for genuine spin SYK- [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The normalized density of states for spin SYK- [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The normalized density of states for spin SYK- [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. The absolute values of averaged ground-state energy as a function of system size [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
read the original abstract

Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-$q$ model using both pure- and mixed-state entanglement measures. We show that von-Neumann and R\'enyi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the R\'enyi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.

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

2 major / 1 minor

Summary. The manuscript investigates information scrambling in the all-to-all interacting spin SYK-q model via pure- and mixed-state entanglement measures. It reports that von Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, a nontrivial dependence of the scrambling rate on interaction order q, system size N, and Hamiltonian scaling, a numerically observed universal relation between Rényi-1/2 mutual information and entanglement negativity for minimal q in the early-time regime, and Page-curve-like behavior in negativity under unequal bipartitions.

Significance. If the central numerical claims hold after addressing finite-size controls, the work would provide concrete evidence that all-to-all multi-body spin models scramble efficiently as diagnosed by multiple entanglement probes and would illustrate the diagnostic power of mixed-state quantities such as negativity for early-time scrambling. The combination of pure-state entropy growth with mixed-state diagnostics is a methodological strength.

major comments (2)
  1. [numerical results on entropy saturation and early-time mutual-information/negativity relation] The claims of saturation 'near Haar-random values' and of a 'universal relation' between Rényi-1/2 mutual information and negativity rest on finite-N numerics (abstract and numerical-results paragraphs). No finite-size scaling collapse, 1/N extrapolation, or direct comparison against the known 1/N corrections to Haar-averaged entanglement quantities is shown; without these controls the saturation values and the apparent universality could be dominated by finite-size artifacts rather than reflecting the thermodynamic or large-N limit.
  2. [negativity under unequal partitioning] The reported Page-curve-like behavior of negativity under unequal subsystem partitioning is presented for specific finite partitions and Hamiltonian scalings. The manuscript does not demonstrate that the birth-spread-death sequence survives in the large-N limit or is robust to the choice of interaction-order scaling, which is load-bearing for the claim that negativity furnishes a generic description of scrambling.
minor comments (1)
  1. [early growth regime discussion] Notation for the Rényi index (Rényi-1/2) and the precise definition of the mutual information should be stated explicitly when first introduced to avoid ambiguity with standard conventions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the two major comments point by point below, indicating the revisions we will incorporate.

read point-by-point responses

  1. Referee: [numerical results on entropy saturation and early-time mutual-information/negativity relation] The claims of saturation 'near Haar-random values' and of a 'universal relation' between Rényi-1/2 mutual information and negativity rest on finite-N numerics (abstract and numerical-results paragraphs). No finite-size scaling collapse, 1/N extrapolation, or direct comparison against the known 1/N corrections to Haar-averaged entanglement quantities is shown; without these controls the saturation values and the apparent universality could be dominated by finite-size artifacts rather than reflecting the thermodynamic or large-N limit.

    Authors: We agree that finite-size controls are necessary to support the claims of saturation near Haar-random values and the apparent universality of the relation. In the revised manuscript we will add 1/N extrapolations of the late-time saturation values for both von Neumann and Rényi entropies, together with direct comparisons to the known 1/N corrections for Haar-averaged quantities. We will also include data for the Rényi-1/2 mutual information versus negativity relation across the available range of N to demonstrate that the observed universality persists with increasing system size. These additions will be placed in a new subsection on finite-size analysis. revision: yes

  2. Referee: [negativity under unequal partitioning] The reported Page-curve-like behavior of negativity under unequal subsystem partitioning is presented for specific finite partitions and Hamiltonian scalings. The manuscript does not demonstrate that the birth-spread-death sequence survives in the large-N limit or is robust to the choice of interaction-order scaling, which is load-bearing for the claim that negativity furnishes a generic description of scrambling.

    Authors: We acknowledge that the birth-spread-death sequence for negativity is currently shown only for finite N and selected q and Hamiltonian scalings. In the revision we will enlarge the data set to include additional system sizes and multiple values of q, explicitly testing robustness under different interaction-order scalings. We will add a paragraph discussing the observed consistency of the sequence within the numerically accessible regime while noting that a complete large-N demonstration would benefit from complementary analytic or approximate methods. This will better delineate the scope of the claim. revision: partial

Circularity Check

0 steps flagged

No significant circularity; claims rest on direct numerical output.

full rationale

The paper reports numerical observations of von-Neumann and Rényi entropy growth to near-Haar saturation and a universal relation between Rényi-1/2 mutual information and negativity in the early-time regime for the SYK-q model. These are presented as simulation results on finite systems under chosen Hamiltonian scalings, with no equations, fitted parameters, or derivations shown that reduce by construction to self-definitions or prior self-citations. No load-bearing self-citation chains, ansatzes smuggled via citation, or renaming of known results appear in the provided text; the central claims remain independent empirical findings rather than tautological restatements of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the work implicitly assumes standard properties of the SYK Hamiltonian and finite-size numerics.

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discussion (0)

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Reference graph

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