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arxiv: 2605.23600 · v1 · pith:MYIAX7XKnew · submitted 2026-05-22 · 🪐 quant-ph · cond-mat.other· cond-mat.quant-gas

Entanglement entropy across the dynamical phase transition in the quantum mathcal{O}(N) model

Frederick del Pozo , Tangi Morvan , Ir\'en\'ee Fr\'erot , Nicolas Cherroret This is my paper

Pith reviewed 2026-05-25 04:23 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.othercond-mat.quant-gas
keywords entanglement entropydynamical phase transitionO(N) modelquantum quenchlarge-N limitentanglement spectrumlogarithmic corrections
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The pith

Quenches at and below criticality in the quantum O(N) model generate gapless entanglement modes and logarithmic corrections to long-time entanglement entropy.

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

The paper shows that the dynamical phase transition leaves clear marks in the subleading structure of entanglement entropy after a quench. While the leading term follows the usual volume law from ballistic spreading, the corrections below and at the critical point come from gapless low-energy modes whose scaling is set by the dynamical exponent. These features are extracted using exact large-N correlation functions on an infinite-slab bipartition. The result ties the infrared entanglement spectrum directly to the post-quench emergence of long-range correlations. Entanglement eigenmodes further display distinctive spatio-temporal patterns and degeneracies that track the different dynamical regimes.

Core claim

The dynamical phase transition of the quantum O(N) model at large N imprints universal signatures on the infrared entanglement spectrum: quenches at and below the critical point produce gapless low-energy entanglement modes together with logarithmic corrections to the long-time entanglement entropy, with the scaling governed by the dynamical exponent of the transition.

What carries the argument

Infinite-slab bipartition geometry together with exact numerical two-point correlation functions in the large-N limit, which isolate the universal infrared entanglement spectrum and its scaling laws.

If this is right

  • The subleading entanglement entropy sharply distinguishes the dynamical regimes even when the volume law is the same.
  • Long-range correlations that develop after the quench directly control the gapless modes in the entanglement spectrum.
  • The entanglement eigenmodes carry additional signatures through their spatial structure and degeneracy pattern.
  • The scaling of the logarithmic corrections is fixed by the same dynamical exponent that governs the order-parameter dynamics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar logarithmic corrections may appear in other models sharing the same dynamical exponent, even outside the strict large-N limit.
  • The slab geometry result suggests that finite-size entanglement calculations in trapped-ion or cold-atom simulators could detect the transition via subleading terms.
  • The degeneracy patterns in the entanglement eigenmodes might offer a practical diagnostic for the dynamical transition in systems where full entropy extraction is hard.

Load-bearing premise

The large-N limit with an infinite-slab cut is enough to capture the universal long-wavelength structure of the entanglement spectrum across the dynamical regimes.

What would settle it

A direct numerical or experimental measurement of the long-time entanglement entropy after a quench below criticality that shows no logarithmic correction (or a correction whose scaling fails to match the dynamical exponent) would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.23600 by Frederick del Pozo, Ir\'en\'ee Fr\'erot, Nicolas Cherroret, Tangi Morvan.

Figure 1
Figure 1. Figure 1: , which displays the time evolution of reff(t) nu￾merically computed from Eqs. (3) and (4) for the three types of quenches in dimension d = 3. In particular, we do observe a decay compatible with reff(t) = 3t 2/16 at the critical quench, while for r < rc the effective mass vanishes exponentially, in accordance with the prediction that a = 0. The different asymptotic behavior of reff(t) across the DPT also … view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Panel (a) Spatial geometry considered in this work. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Main panel: Entanglement entropy per unit area [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Panel a: Late-time entanglement spectrum [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Prefactor of the entanglement dispersion, [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Inverse of the entanglement gap ∆( [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Entanglement entropy per [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Time evolution of the dispersion at [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Spatial distributions of the entanglement eigenvectors [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
read the original abstract

We demonstrate that the dynamical phase transition of the quantum $\mathcal{O}(N)$ model at large $N$ leaves universal fingerprints in the infrared structure of the entanglement spectrum. While the leading contribution to the entanglement entropy at long time follows the conventional volume law associated with ballistic entanglement spreading, its subleading behavior sharply distinguishes the different dynamical regimes. Specifically, quenches at and below the critical point generate gapless low-energy entanglement modes together with logarithmic corrections to the long-time entanglement entropy, whose scaling is governed by the dynamical exponent of the transition. Using an infinite-slab bipartition geometry and exact numerical correlation functions in the large-$N$ limit, we characterize these scaling laws across the dynamical phase diagram and relate them to the emergence of long-range correlations during the post-quench dynamics. We further show that the entanglement eigenmodes themselves reveal characteristic signatures of the dynamical phase transition through their spatio-temporal structure and degeneracy properties.

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

0 major / 1 minor

Summary. The manuscript studies entanglement entropy following quantum quenches in the O(N) model at large N. It reports that quenches at and below the critical point produce gapless low-energy entanglement modes together with logarithmic corrections to the long-time volume-law entanglement entropy, with the correction coefficient set by the dynamical exponent of the transition. These features are extracted from exact numerical two-point correlation functions using an infinite-slab bipartition geometry, and the entanglement eigenmodes are shown to carry additional signatures of the dynamical transition through their spatio-temporal structure and degeneracy.

Significance. If the central results hold, the work establishes a direct link between dynamical phase transitions and the infrared structure of the entanglement spectrum, providing a new, falsifiable diagnostic for non-equilibrium criticality. A notable strength is the exact large-N solvability, which supplies parameter-free numerical correlation functions and allows direct extraction of the sub-leading logarithmic term without post-hoc fitting or uncontrolled approximations.

minor comments (1)
  1. The abstract states that the scaling is 'governed by the dynamical exponent' but does not quote the explicit value or functional form used for the exponent in the numerical extractions; adding this would improve immediate readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript and for recommending acceptance. The summary accurately captures the central results on the infrared structure of the entanglement spectrum across the dynamical phase transition.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The manuscript constructs post-quench two-point functions exactly in the large-N limit, assembles the reduced correlation matrix for the infinite-slab bipartition, and extracts the sub-leading logarithmic term numerically from the entanglement spectrum. The dynamical exponent enters the scaling through the known dispersion of the gapless modes generated by the quench; this relation is not obtained by fitting a parameter to the target quantity nor by renaming an input. No self-citation is invoked as a uniqueness theorem or to smuggle an ansatz, and the central claims remain independent of the reported results themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the large-N limit yields exact correlation functions whose infrared structure faithfully captures the entanglement scaling; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The large-N limit allows exact computation of correlation functions that determine the entanglement spectrum.
    The paper invokes this limit to obtain the reported scaling laws and gapless modes.

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Reference graph

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