{"id":"8e71125d-bbca-4483-b5f5-ef4c48da9741","arxiv_id":"2602.00900","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Asymmetry monotones associated with collective spin generators capture the onset of dynamical quantum phase transitions in the quenched Lipkin-Meshkov-Glick model and correlate with entropy production.","lead":"This paper connects measures of quantum asymmetry to the detection of dynamical quantum phase transitions in a specific spin model. It suggests asymmetry can serve as an indicator of critical behavior linked to symmetry changes and entropy production.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Generalization of asymmetry monotones as DQPT indicators rests on untested extrapolation beyond LMG collective-spin symmetry","rationale":"The reader's weakest assumption directly identifies the same generalization gap. Because the provided abstract supplies no cross-model data and the full text is referenced only as source, the concern is scoped to the logical scope of the claim rather than any internal derivation error. This moves the verdict from UNVERDICTED to CONDITIONAL pending the proposed check.","tokens_in":1688,"tokens_out":354,"duration_ms":26021,"concrete_test":"Construct the analogous asymmetry monotone using the local transverse-field generator on the quenched 1D Ising chain (L=20–40 sites) across its known DQPT critical point; recompute the time-averaged asymmetry and test whether its non-analyticity or peak coincides with the Loschmidt-echo singularity within numerical precision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The strongest claim asserts that asymmetry monotones tied to collective spin generators 'faithfully capture the onset of DQPTs' and supply a 'unifying concept' for dynamical criticality. This holds in the quenched LMG model by construction, since the generators align with the model's global SU(2) symmetry whose dynamical breaking/restoration is already known to control the Loschmidt-echo non-analyticities. The load-bearing step is therefore the implicit assumption that the same construction remains faithful once the symmetry is no longer all-to-all or collective, i.e., in short-range or locally interacting Hamiltonians where no single set of generators commutes with the full dynamics. Without an explicit check in at least one such model, the 'robust and physically transparent indicator' status is model-specific rather than general.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","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.","tokens_in":1826,"tokens_out":576,"duration_ms":50612,"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":[{"comment":"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.","section":"Abstract and concluding section"},{"comment":"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.","section":"Results section on time-averaged asymmetry"}],"minor_comments":[{"comment":"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.","section":"Methods"},{"comment":"Add a brief discussion of the model's all-to-all interaction range when stating implications for 'many-body systems exhibiting DQPTs'.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is tightly focused on a single exactly solvable model; this limits the strength of the 'unifying framework' language for a broad-audience journal but does not affect technical soundness within the LMG setting."},"author_rebuttal":{"model":"grok-4.3","summary":"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.","responses":[{"response":"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_made":"partial","referee_comment":"[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."},{"response":"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_made":"yes","referee_comment":"[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."}],"tokens_in":1395,"tokens_out":682,"duration_ms":32092,"standing_objections":["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"]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this work demonstrates a concrete link in the quenched Lipkin-Meshkov-Glick model: asymmetry monotones built from collective spin generators pick up the dynamical critical point, line up with the Loschmidt-echo non-analyticities, and coincide with peaks in entropy production. They also report that the time average of the asymmetry shows clear signatures across the transition. That is a direct, model-specific result worth noting for people who already work with the LMG or similar collective-spin systems. The calculations appear to be carried out honestly in a solvable setting where the symmetry is global, so the correspondence is not surprising but still useful to see spelled out with the thermodynamic tie-in. What the paper does well is keep the focus on one standard model and extract a transparent information-theoretic signature that matches existing order parameters. The soft spot is the jump to generality. The abstract calls asymmetry a robust and unifying indicator for DQPTs, yet everything stays inside the all-to-all LMG case where the chosen generators commute with the full dynamics by construction. The stress-test concern holds: once the interactions become short-range or local, no single set of collective generators will capture the symmetry breaking in the same way, and the paper does not appear to test that regime. Without at least one additional example outside the collective-spin limit, the robustness claim is model-dependent rather than general. This is aimed at researchers in nonequilibrium quantum many-body physics who are already looking at information measures or symmetry in DQPTs. The concrete numerics and the entropy-production link give it enough substance to go to referees rather than a desk reject; they can ask for clarification on scope and any extra checks if needed. I would send it out for peer review.","headline":"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.","tokens_in":2309,"tokens_out":431,"would_cite":false,"duration_ms":38700,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean","rs_theorem":"reality_from_one_distinction","paper_passage":"asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries"},{"relation":"unclear","rs_module":"IndisputableMonolith/Cost/FunctionalEquation.lean","rs_theorem":"washburn_uniqueness_aczel","paper_passage":"FL(ρ) = ∥[ρ, L]∥1 ... time-averaged asymmetry exhibits clear signatures of the dynamical critical point"}],"headline":"Asymmetry monotones for DQPTs in LMG model unrelated to RS distinction-forcing or J-cost","alignment":"orthogonal","rationale":"Paper's core machinery (ℓ1-norm commutator FL(ρ)=∥[ρ,L]∥1 w.r.t. collective spin generators Jx,Jy,Jz tracking symmetry restoration across quenches) operates entirely within quantum many-body dynamics and resource theory of asymmetry; RS framework derives J(x)=½(x+x⁻¹)−1, φ, 8-tick periodicity and spacetime from bare distinguishability (reality_from_one_distinction, AbsoluteFloorClosure, Cost.FunctionalEquation) with zero adjustable parameters and no reference to Loschmidt echoes, collective-spin generators or entropy-production peaks.","tokens_in":50033,"confidence":"high","tokens_out":332,"duration_ms":13811,"cache_read_input_tokens":32896,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Asymmetry monotones detect the onset of dynamical quantum phase transitions by tracking symmetry restoration and breaking in the quenched Lipkin-Meshkov-Glick model.","keywords":["dynamical quantum phase transitions","quantum asymmetry","Lipkin-Meshkov-Glick model","symmetry breaking","nonequilibrium thermodynamics","entropy production","quantum criticality"],"falsifier":"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.","tokens_in":2585,"feed_emoji":"⚛","tokens_out":651,"duration_ms":25604,"temperature":0.7,"pith_summary":"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.","feed_headline":"Asymmetry monotones mark dynamical quantum criticality","feed_subtitle":"In the quenched Lipkin-Meshkov-Glick model, time-averaged asymmetry tracks the onset of DQPTs and aligns with peaks in entropy production.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"fun_headline_variants":["Asymmetry captures DQPT onset in quenched LMG model","Time-averaged asymmetry signals LMG dynamical criticality","Asymmetry links DQPT to entropy production peaks","Collective spin asymmetry detects DQPT in LMG model"],"cache_read_input_tokens":64,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Asymmetry captures DQPT onset in quenched LMG model","Time-averaged asymmetry signals LMG dynamical criticality","Asymmetry links DQPT to entropy production peaks","Collective spin asymmetry detects DQPT in LMG model"]},"model":"grok-4.3","cost_usd":0.012194,"raw_usage":{"total_tokens":5218,"prompt_tokens":627,"num_sources_used":0,"completion_tokens":60,"cost_in_usd_ticks":121940500,"prompt_tokens_details":{"text_tokens":627,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":4531,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":627,"tokens_out":60,"duration_ms":56456,"temperature":1.0,"reasoning_tokens":4531,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-21T13:26:52.448893+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"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.","supporting_citations":[],"review_version":1}