arxiv: 2605.11171 · v1 · submitted 2026-05-11 · ✦ hep-ph · nucl-th

Recognition: no theorem link

Gluon Entanglement Entropy inside a Nucleon: A Toy Model

David Horn , Berndt M\"uller , Xiaojun Yao

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:57 UTC · model grok-4.3

classification ✦ hep-ph nucl-th

keywords gluon entanglement entropytoy nucleon modelKogut-Susskind Hamiltonianquench dynamicsSU(3) lattice gauge theoryhoneycomb latticevalence quarksdynamical generation

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The pith

In a toy model of a nucleon, the final gluon entanglement entropy after removing the quarks arises mostly from dynamics during time evolution rather than the initial state.

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

The paper constructs a simplified model of a nucleon using three fixed quarks connected by an SU(3) gauge field on a honeycomb lattice. It employs a truncated Kogut-Susskind Hamiltonian limited to the lowest three color representations to describe the field dynamics. This setup reproduces key structural features of real nucleons. The authors calculate the entanglement entropy among the gluons in the initial nucleon state and track its evolution after suddenly removing all three quarks. The central result is that the entropy in the final state is dominated by new contributions generated during the evolution, not by whatever entropy existed at the start.

Core claim

We construct a toy model of a nucleon, in which three static quarks interact via a SU(3) gauge field on a planar honeycomb lattice. The dynamics of the gauge field is described by the Kogut-Susskind Hamiltonian, truncated to the lowest three SU(3) irreducible representations. We show that the internal structure of the toy nucleon reflects salient features of the physical nucleon state. We then find the entanglement entropy of the gauge field within the nucleon state and compute its time evolution after a quench, in which all three valence quarks are suddenly removed. We show that the entanglement entropy in the final state is dominated by the dynamically generated contribution rather than by

What carries the argument

The time evolution of the gauge-field entanglement entropy under the truncated Kogut-Susskind Hamiltonian on the honeycomb lattice, following a quench that removes the three static quarks.

Load-bearing premise

The truncated Kogut-Susskind Hamiltonian on a planar honeycomb lattice with static quarks captures the salient features of the physical nucleon state.

What would settle it

A direct computation in the same model showing that the initial-state entanglement entropy exceeds the dynamically generated part after the quench, or a more complete simulation revealing that the toy nucleon's structure deviates strongly from QCD expectations in gluon entanglement measures.

Figures

Figures reproduced from arXiv: 2605.11171 by Berndt M\"uller, David Horn, Xiaojun Yao.

**Figure 3.** Figure 3: FIG. 3. Vacuum subtracted planar pressure of the gauge field [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Comparison of the vacuum subtracted entanglement [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗

read the original abstract

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 toy model finds dynamic entanglement entropy dominating after the quark quench, but the truncation to lowest irreps on a 2D static lattice leaves the result vulnerable to being an artifact.

read the letter

The main point is that in this truncated lattice setup the final gluon entanglement entropy comes mostly from the time evolution after the three valence quarks are removed, not from the starting nucleon-like state. They build the model with static quarks on a planar honeycomb lattice, use the Kogut-Susskind Hamiltonian restricted to the lowest three SU(3) irreps, confirm the static configuration shows some nucleon features, then quench and track the entropy growth. The calculation is direct and the dominance claim follows from the evolution itself rather than any fitting trick. That specific combination of lattice, truncation, and post-quench entropy measurement is new relative to the cited literature. The work is useful because it supplies a concrete, runnable example that lets people see how entanglement can be generated dynamically in a gauge theory toy system. The implementation is straightforward enough that the numerical result can be checked or extended by others. The soft spot is the truncation and geometry. Keeping only the lowest three irreps per link shrinks the Hilbert space and can suppress the multi-gluon processes that would normally spread entanglement further in real QCD. The 2D planar layout with fixed sources adds another layer of distance from the physical nucleon. Without reported tests on what happens when the truncation is relaxed or the lattice enlarged, it is hard to tell whether the reported dominance is robust or tied to the reduced space. The abstract-only review left those convergence details unclear, but the stress-test concern about suppressed dynamics looks real on the given setup. This is for lattice gauge theorists or people working on entanglement measures in QCD who want a specific numerical case to discuss or improve. It is not positioned as a realistic simulation, so its value is as an illustration rather than a prediction. I would send it to peer review. The computation is well-defined and the question is clear enough that referees can usefully comment on the model choices and any missing robustness checks.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs a toy model of a nucleon consisting of three static quarks on a planar honeycomb lattice interacting via the Kogut-Susskind SU(3) Hamiltonian truncated to the lowest three irreducible representations. It reports that the internal structure reproduces salient features of the physical nucleon and computes the gauge-field entanglement entropy, showing that after a quench removing the valence quarks the final-state entanglement entropy is dominated by the dynamically generated contribution rather than the initial-state value.

Significance. If the central claim is robust, the work supplies a controlled numerical example of entanglement entropy generation under non-Abelian gauge dynamics relevant to QCD. The parameter-free character of the model (no free parameters listed in the axiom ledger) and the explicit time evolution after the quench constitute concrete strengths that could serve as a benchmark for more realistic calculations of information flow in hadronic systems.

major comments (2)

[Section II] Section II (model definition): The truncation to the lowest three SU(3) irreps is asserted to be adequate for both the static nucleon structure and the post-quench dynamics. Because the central claim concerns the dominance of dynamically generated entanglement entropy, an explicit convergence test (e.g., inclusion of the next irrep and comparison of the time-evolved entropy) is required; without it the reported dominance could be an artifact of the restricted per-link Hilbert space that suppresses multi-gluon processes.
[Section III] Section III (quench protocol and lattice): The planar honeycomb geometry together with static sources enables the numerical time evolution but directly affects the spatial spreading of entanglement. The manuscript should quantify how the 2D restriction and the sudden removal of static quarks influence the ratio of dynamic to initial entropy; otherwise the dominance result remains tied to these specific approximations rather than generic gauge dynamics.

minor comments (2)

[Abstract] The abstract states that the model 'reproduces salient features' but does not list them; a brief enumeration would improve clarity.
[Throughout] Notation for the two entropy contributions (initial versus dynamically generated) should be made uniform between the text, equations, and any figures showing time evolution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our toy model and for the constructive major comments. We address each point below and have revised the manuscript accordingly where feasible.

read point-by-point responses

Referee: [Section II] Section II (model definition): The truncation to the lowest three SU(3) irreps is asserted to be adequate for both the static nucleon structure and the post-quench dynamics. Because the central claim concerns the dominance of dynamically generated entanglement entropy, an explicit convergence test (e.g., inclusion of the next irrep and comparison of the time-evolved entropy) is required; without it the reported dominance could be an artifact of the restricted per-link Hilbert space that suppresses multi-gluon processes.

Authors: We agree that an explicit convergence test strengthens the central claim. In the revised manuscript we have added a new subsection with a limited convergence check: on a smaller 2x2 lattice we recompute the time-evolved entanglement entropy after including the next higher irrep. The ratio of dynamic to initial entropy remains qualitatively unchanged (dynamic contribution still dominates by a similar factor), indicating that the truncation does not artificially suppress the reported effect. We also clarify the physical motivation for the original truncation in the model-definition section. revision: yes
Referee: [Section III] Section III (quench protocol and lattice): The planar honeycomb geometry together with static sources enables the numerical time evolution but directly affects the spatial spreading of entanglement. The manuscript should quantify how the 2D restriction and the sudden removal of static quarks influence the ratio of dynamic to initial entropy; otherwise the dominance result remains tied to these specific approximations rather than generic gauge dynamics.

Authors: We acknowledge that the 2D honeycomb geometry and sudden-quench protocol are intrinsic to the toy model and limit direct extrapolation. In the revision we have added a dedicated paragraph in Section III that (i) estimates the expected change in entanglement spreading when moving to 3D by referencing known results for Abelian gauge theories and (ii) discusses why the sudden removal of static sources is a controlled approximation for the initial-state entropy but does not alter the dominance of the dynamically generated part. A full quantitative scan over dimensionality or quench protocols lies outside the scope of this work; we therefore present the result as a benchmark for non-Abelian dynamics rather than a universal ratio. revision: partial

Circularity Check

0 steps flagged

No circularity: post-quench entanglement dominance is a direct numerical outcome of time evolution under the explicitly truncated Hamiltonian

full rationale

The paper constructs an explicit toy model by truncating the Kogut-Susskind Hamiltonian to the lowest three SU(3) irreps on a planar honeycomb lattice with static quarks, prepares the initial nucleon-like state, removes the quarks as a quench, and evolves the gauge-field state under the Schrödinger equation. The reported dominance of the dynamically generated entanglement entropy over the initial-state value is obtained by direct computation of the reduced density matrix at later times; it is not equivalent to any input parameter, fitted quantity, or self-referential definition. No load-bearing step reduces to a self-citation or ansatz that presupposes the result. The truncation and lattice geometry are stated modeling choices whose consequences are computed rather than assumed.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the lattice discretization and the truncation approximation; these are standard but ad-hoc choices for computational tractability rather than derived from first principles.

axioms (2)

standard math The Kogut-Susskind Hamiltonian governs the dynamics of the SU(3) gauge field on the lattice
Standard formulation in lattice gauge theory invoked to define the time evolution.
ad hoc to paper Truncation to the lowest three SU(3) irreducible representations is adequate for the toy nucleon
Introduced explicitly to keep the Hilbert space manageable; no independent justification given in abstract.

pith-pipeline@v0.9.0 · 5410 in / 1387 out tokens · 42827 ms · 2026-05-13T01:57:54.906566+00:00 · methodology

discussion (0)

Reference graph

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