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REVIEW 2 major objections 2 minor 44 references

Asymmetry and dynamical criticality

T0 review · 2 major / 2 minor · reviewed 2026-05-21 · grok-4.3

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Pith's one-line read Asymmetry monotones detect the onset of dynamical quantum phase transitions by tracking symmetry restoration and breaking in the quenched Lipkin-Meshkov-Glick model.

desk verdict The paper shows asymmetry monotones track DQPTs in the LMG model with some correspondence to entropy production, but the broader unifying claim rests on the model's global symmetry and lacks checks elsewhere. read the letter →

arxiv 2602.00900 v2 pith:IQ46SDQA submitted 2026-01-31 quant-ph

Andesson B. Nascimento , Lucas Chibebe Céleri This is my paper · ORCID
classification quant-ph
keywords dynamicalquantumphasetransitionsasymmetryLipkin-Meshkov-Glickmodelsymmetrybreakingnonequilibriumthermodynamicsentropyproductioncriticality
checked against Foundation.AbsoluteFloorClosureCost.FunctionalEquation
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

This paper connects measures of quantum asymmetry to the detection of dynamical quantum phase transitions in a many-body spin model. It shows that asymmetry monotones built from collective spin generators register the points where underlying symmetries are dynamically restored or broken during a quench. These monotones produce clear signatures at the critical point when averaged over time, matching the behavior of the dynamical order parameter. The same asymmetry peaks coincide with maximum entropy production, establishing a direct tie between symmetry dynamics and thermodynamic irreversibility.

What carries the argument

Asymmetry monotones associated with collective spin generators, which quantify the extent to which a state deviates from invariance under symmetry transformations and thereby register the dynamical breaking or restoration of symmetry during a quench.

What would settle it

Compute the time-averaged asymmetry in a second model known to host DQPTs, such as the transverse-field Ising chain, and check whether its peaks or kinks coincide with the independently known dynamical critical point.

Watch

Extended reading notes

Core claim

In the quenched Lipkin-Meshkov-Glick model, asymmetry measures associated with collective spin generators faithfully capture the onset of dynamical quantum phase transitions, reflecting the dynamical restoration or breaking of underlying symmetries; the time-averaged asymmetry exhibits clear signatures of the dynamical critical point in close correspondence with both the dynamical order parameter and the behavior of entropy production.

Load-bearing premise

That asymmetry measures built specifically from collective spin generators in this model will continue to mark dynamical quantum criticality when applied to other many-body systems that exhibit DQPTs.

Editorial extensions

If this is right

  • Time-averaged asymmetry can function as an alternative diagnostic for the location of the dynamical critical point.
  • Peaks in asymmetry generation line up with intervals of maximal entropy production across the transition.
  • Asymmetry supplies a single quantifier that links symmetry properties, information-theoretic measures, and nonequilibrium thermodynamics.
  • The approach yields a physically transparent indicator that does not require construction of a conventional dynamical order parameter.

Reading between the lines

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

  • The same asymmetry construction could be tested in open quantum systems to see whether it still flags criticality when dissipation is present.
  • If the link to entropy production holds more generally, asymmetry peaks might help identify efficient quench protocols that minimize irreversibility.
  • In systems where order parameters are difficult to define, asymmetry monotones might provide a practical route to locate dynamical critical points.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript establishes a connection between measures of quantum asymmetry and dynamical quantum phase transitions (DQPTs) by focusing on the quenched Lipkin-Meshkov-Glick (LMG) model. It demonstrates that asymmetry monotones associated with collective spin generators capture the onset of DQPTs, reflect dynamical symmetry restoration or breaking, and that the time-averaged asymmetry exhibits signatures of the dynamical critical point in correspondence with the dynamical order parameter and entropy production; a quantitative link is also drawn between asymmetry generation and thermodynamic irreversibility.

Significance. If the reported correspondences hold under the model's symmetries, the work supplies a symmetry-based, information-theoretic quantifier that complements traditional order parameters for DQPTs and explicitly ties asymmetry peaks to maximal entropy production. This offers a physically transparent bridge between symmetry properties, nonequilibrium thermodynamics, and criticality in collective-spin systems, with potential utility for other models sharing global SU(2) symmetry.

major comments (2)
  1. [Abstract and concluding section] Abstract and concluding section: the claim that asymmetry monotones supply a 'robust and physically transparent indicator' and 'unifying concept' for DQPTs is demonstrated by construction for the LMG model whose global SU(2) symmetry is already known to control Loschmidt-echo non-analyticities; the manuscript does not contain an explicit check or discussion of a short-range or locally interacting Hamiltonian where no single set of collective generators commutes with the full dynamics, which is load-bearing for the broader framing.
  2. [Results section on time-averaged asymmetry] Results section on time-averaged asymmetry: the reported 'clear signatures' of the dynamical critical point are stated to be in close correspondence with the order parameter, but without a quantitative comparison (e.g., location of the asymmetry peak versus the known DQPT critical value, finite-size scaling, or overlap with Loschmidt-echo singularities) it is difficult to assess whether the indicator is faithful or merely qualitatively consistent.
minor comments (2)
  1. [Methods] Clarify the precise definition of the asymmetry monotone (relative entropy of asymmetry or another quantifier) and its relation to the collective spin generators in the methods or appendix.
  2. [Discussion] Add a brief discussion of the model's all-to-all interaction range when stating implications for 'many-body systems exhibiting DQPTs'.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and insightful report. The comments highlight important aspects of the scope and quantitative support for our claims. We address each major comment point by point below, providing clarifications and indicating revisions where we have strengthened the manuscript without altering the core results for the LMG model.

read point-by-point responses

  1. Referee: [Abstract and concluding section] Abstract and concluding section: the claim that asymmetry monotones supply a 'robust and physically transparent indicator' and 'unifying concept' for DQPTs is demonstrated by construction for the LMG model whose global SU(2) symmetry is already known to control Loschmidt-echo non-analyticities; the manuscript does not contain an explicit check or discussion of a short-range or locally interacting Hamiltonian where no single set of collective generators commutes with the full dynamics, which is load-bearing for the broader framing.

    Authors: We agree that the explicit demonstration is constructed for the LMG model, where the global SU(2) symmetry of the collective spin operators directly controls the Loschmidt-echo non-analyticities and the associated DQPTs. This model was selected precisely because it allows a transparent mapping between the asymmetry monotones (defined with respect to the collective generators) and the dynamical symmetry breaking/restoration. The broader framing in the abstract and conclusions is motivated by the fact that many collective-spin systems share this global symmetry structure, positioning asymmetry as a symmetry-based quantifier that complements order parameters. To address the concern, we have revised the concluding section to include an explicit discussion of the role of the model's symmetries, clarifying that the approach relies on the existence of collective generators that commute with the Hamiltonian. We further note the limitations for short-range or locally interacting systems lacking such global commuting generators, framing this as an avenue for future investigation rather than a claim of immediate generality. The core results and physical transparency for the LMG case remain unchanged. revision: partial

  2. Referee: [Results section on time-averaged asymmetry] Results section on time-averaged asymmetry: the reported 'clear signatures' of the dynamical critical point are stated to be in close correspondence with the order parameter, but without a quantitative comparison (e.g., location of the asymmetry peak versus the known DQPT critical value, finite-size scaling, or overlap with Loschmidt-echo singularities) it is difficult to assess whether the indicator is faithful or merely qualitatively consistent.

    Authors: We thank the referee for this suggestion, which improves the rigor of the presentation. In the revised manuscript, we have expanded the results section on the time-averaged asymmetry to include quantitative comparisons. Specifically, we now report the location of the asymmetry peak relative to the known critical value of the DQPT in the quenched LMG model (showing close numerical agreement), discuss the finite-size scaling of the asymmetry signatures, and examine their overlap with the Loschmidt-echo singularities. These additions demonstrate that the time-averaged asymmetry faithfully captures the dynamical critical point, with peaks aligning to within a few percent of the established critical point and exhibiting consistent scaling behavior. revision: yes

standing simulated objections not resolved
  • Explicit numerical check or demonstration for a short-range or locally interacting Hamiltonian where no single set of collective generators commutes with the full dynamics

Circularity Check

0 steps flagged · score 2.0 of 10

Demonstration in LMG model is self-contained with no load-bearing reductions

full rationale

The paper focuses on explicit demonstrations within the quenched Lipkin-Meshkov-Glick model, showing that asymmetry monotones associated with collective spin generators capture DQPT onset by direct correspondence to the dynamical order parameter and entropy production. No equations or claims reduce by construction to fitted parameters, self-definitions, or unverified self-citations; the central results are presented as model-specific calculations that align with known symmetry-breaking behavior rather than being forced by the inputs themselves. Generalization remarks remain interpretive and do not alter the independence of the reported derivations.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

Abstract provides no explicit free parameters, invented entities, or ad-hoc axioms; relies on standard quantum many-body theory for the LMG model.

assumptions (1)
  • standard math Standard principles of quantum mechanics and many-body spin models apply to the quenched Lipkin-Meshkov-Glick Hamiltonian.
    The demonstration uses the established LMG model without introducing new postulates.

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Cite this review

Pith. "Pith review of Asymmetry and dynamical criticality." pith.science (2026). https://pith.science/paper/IQ46SDQA

@misc{pith2026260200900,
  author       = {Pith},
  title        = {Pith review of: Asymmetry and dynamical criticality},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IQ46SDQA}},
  note         = {Machine review of arXiv:2602.00900}
}
read the original abstract

Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.

Figures

Figures reproduced from arXiv: 2602.00900 by the authors.

Figure 1
Figure 1. FIG. 1: Dynamical order parameter [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Time evolution of the asymmetry measure [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Time average of the asymmetry measure [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Time average of Entropy Production [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Time average of the asymmetry measure [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Dynamic order parameter [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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Reference graph

Works this paper leans on

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