{"id":"c4620538-ffcd-40a6-bfe2-e8db0341990d","arxiv_id":"2605.20656","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"In the random-field XXZ model, Wehrl-Rényi entropy growth for z-polarized product states shows non-monotonic dependence on initial entanglement, with the first regime set by local integrals of motion and the second by inter-site correlations.","lead":"This paper studies how entanglement entropy grows in many-body localized quantum systems when initial states are prepared with varying amounts of entanglement. It traces the non-monotonic behavior to specific properties like magnetization and inter-site correlations in a standard disordered spin model.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Chosen disorder strength and finite sizes in random-field XXZ may not confirm deep MBL regime required to attribute regimes to LIOMs","rationale":"The reader's weakest assumption already flags the model parameters as the key vulnerability. My concern is a direct technical sharpening of that point: the LIOM interpretation is load-bearing for the physical-origin claim, and level statistics provide a standard, falsifiable check that would either validate or undermine the attribution without requiring new observables.","tokens_in":1742,"tokens_out":369,"duration_ms":34431,"concrete_test":"For each disorder strength and L used in the main figures, compute the disorder-averaged level spacing ratio <r> over at least 1000 eigenstates and 500 realizations; if <r> remains above ~0.45 (closer to GOE than Poisson), rerun the Wehrl-Rényi growth curves at stronger disorder where <r> < 0.3 and check whether the non-monotonic z-polarized regimes survive.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim attributes the first non-monotonic regime in Wehrl-Rényi entropy growth to finite magnetization from local integrals of motion (LIOMs) and the second to inter-site correlations. For this to hold, the random-field XXZ Hamiltonian at the simulated parameters must be in the MBL phase where LIOMs are well-defined and approximately conserved. The abstract and reader's weakest assumption reference specific disorder strength and system size, but without explicit MBL diagnostics (e.g., Poisson level statistics, eigenstate entanglement scaling, or localization length << L), the observed z vs. x/y contrast and non-monotonicity could instead reflect slow thermalization, Griffiths effects, or prethermal dynamics that occur outside true MBL.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper studies entanglement dynamics in many-body localized (MBL) systems prepared from structured initial states, obtained by evolving product states under a chaotic Hamiltonian before quenching to the random-field XXZ model. It reports that the Wehrl-Rényi entropy (used as a proxy for multipartite entanglement) exhibits non-monotonic growth with increasing initial entanglement for z-polarized states, with the first regime attributed to finite magnetization from local integrals of motion (LIOMs) and the second to inter-site correlations; x/y-polarized states instead show monotonic decay. This refines earlier observations on total Rényi entanglement entropy.","tokens_in":1904,"tokens_out":562,"duration_ms":41222,"significance":"If the central attribution holds, the work supplies a useful separation of magnetization versus correlation contributions to entanglement growth in MBL systems and demonstrates the utility of the Wehrl-Rényi entropy for tracking multipartite structure. Such distinctions could help characterize the role of LIOMs in realistic finite-size numerics.","major_comments":[{"comment":"§3 (Numerical setup): The chosen disorder strength and system sizes for the random-field XXZ chain are not accompanied by standard MBL diagnostics (Poisson level statistics, eigenstate entanglement scaling, or localization length ≪ L). Because the first regime is explicitly attributed to conserved magnetization from LIOMs, the absence of these checks leaves open the possibility that the observed non-monotonicity arises from slow thermalization or prethermal effects instead.","section":"§3"},{"comment":"Results on Wehrl-Rényi entropy (around the discussion of net growth for z-polarized states): The mapping from the second regime to inter-site correlations is stated but not supported by an explicit decomposition or comparison against a magnetization-subtracted observable; without this, the separation between the two regimes remains interpretive rather than quantitative.","section":"Results on Wehrl-Rényi entropy"}],"minor_comments":[{"comment":"Figure captions and methods: Add the number of disorder realizations and any error-bar information; the current presentation leaves the statistical robustness of the non-monotonic curves unclear.","section":"Figures"},{"comment":"Notation: Define the precise normalization or subtraction used for “net growth” of the Wehrl-Rényi entropy when it is first introduced in the main text.","section":"Main text"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a reasonable fit for a quantum-information or condensed-matter journal, but the MBL-diagnostic gap is the primary load-bearing concern; once addressed, the paper would be substantially stronger."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of our manuscript and for the constructive comments. We address each major point below and describe the revisions we will make to the manuscript.","responses":[{"response":"We agree that explicit MBL diagnostics would strengthen the attribution to local integrals of motion and help rule out alternative explanations. In the revised manuscript we will add the average level-spacing ratio (confirming Poisson statistics), the scaling of eigenstate entanglement entropy with system size, and an estimate of the localization length for the disorder strengths and system sizes used in the numerics.","revision_made":"yes","referee_comment":"[§3] §3 (Numerical setup): The chosen disorder strength and system sizes for the random-field XXZ chain are not accompanied by standard MBL diagnostics (Poisson level statistics, eigenstate entanglement scaling, or localization length ≪ L). Because the first regime is explicitly attributed to conserved magnetization from LIOMs, the absence of these checks leaves open the possibility that the observed non-monotonicity arises from slow thermalization or prethermal effects instead."},{"response":"The separation is currently supported by the contrasting dynamics: non-monotonic net growth appears only for z-polarized states (which carry finite magnetization tied to LIOMs) while x/y-polarized states exhibit monotonic decay. We nevertheless acknowledge that an explicit quantitative decomposition would make the claim more rigorous. In the revision we will include a direct comparison against a magnetization-subtracted observable to quantify the inter-site correlation contribution in the second regime.","revision_made":"yes","referee_comment":"[Results on Wehrl-Rényi entropy] Results on Wehrl-Rényi entropy (around the discussion of net growth for z-polarized states): The mapping from the second regime to inter-site correlations is stated but not supported by an explicit decomposition or comparison against a magnetization-subtracted observable; without this, the separation between the two regimes remains interpretive rather than quantitative."}],"tokens_in":1425,"tokens_out":428,"duration_ms":25171,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main thing to know is that this work takes the non-monotonic entanglement growth seen in Zhang et al. and attributes the first regime to leftover magnetization tied to local integrals of motion and the second to inter-site correlations. They show this pattern in the Wehrl-Rényi entropy for z-polarized product states after a quench, while x/y polarizations produce only monotonic decay. The Wehrl-Rényi measure is used because it tracks multipartite entanglement more directly than standard Rényi entropy alone. This gives a cleaner split between the two physical origins than the earlier observation of non-monotonicity by itself. The directional contrast serves as a useful internal check that the behavior is not generic to all initial polarizations. The numerics appear to support the claimed regimes at the disorder strengths they simulate. On the soft side, the attribution to LIOMs assumes the parameters place the system well inside the MBL phase. Without explicit diagnostics such as level statistics or localization length scaling in the text, it remains possible that slow thermalization or prethermal effects contribute instead. The abstract also omits error bars and finite-size checks, so those controls would need to be verified to confirm the regimes are robust rather than artifacts of small systems. This paper is aimed at theorists working on entanglement dynamics and information retention in disordered many-body systems. Readers already following MBL and initial-state engineering will get the most from the mechanistic distinction. It deserves peer review because the regime separation is a concrete step beyond the cited prior result, even if the MBL confirmation and scaling details may require tightening.","headline":"The paper separates magnetization from inter-site correlations as the drivers of two regimes in Wehrl-Rényi entropy growth for z-polarized structured states in the random-field XXZ model.","tokens_in":2390,"tokens_out":399,"would_cite":false,"duration_ms":33704,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"MBL entanglement growth via LIOMs and Wehrl-Rényi entropy in random-field XXZ shows no RS-shaped cost or ladder structure","alignment":"orthogonal","rationale":"The paper's central machinery is numerical simulation of Rényi and Wehrl-Rényi entropy growth under structured initial states in the 1D random-field XXZ model, attributing non-monotonic regimes to LIOM magnetization relaxation versus inter-site correlations. This is standard many-body localization phenomenology with no reference to J-cost functions, ratio symmetry, golden-ratio identities, φ-ladder spacings, 8-tick periodicity, or parameter-free constant derivations. RS framework (e.g., reality_from_one_distinction, Cost.FunctionalEquation.washburn_uniqueness_aczel, Foundation.DimensionForcing) has no opinion on this domain of quantum dynamics calculations.","tokens_in":55139,"confidence":"high","tokens_out":193,"duration_ms":10580,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Structured initial states produce non-monotonic entanglement growth in many-body localized systems when product states are polarized along z.","keywords":["many-body localization","entanglement growth","Wehrl-Rényi entropy","structured initial states","random-field XXZ model","local integrals of motion","multipartite entanglement"],"falsifier":"Numerical or experimental data showing strictly monotonic Wehrl-Rényi entropy growth versus initial entanglement for z-polarized states, without the reported up-then-down behavior across a range of preparation times, would falsify the claimed two-regime structure.","tokens_in":2634,"feed_emoji":"","tokens_out":511,"duration_ms":39321,"temperature":0.7,"pith_summary":"The paper examines how varying the initial entanglement in structured states affects subsequent entanglement growth in many-body localized systems. Using the random-field XXZ model, it demonstrates that the net growth of Wehrl-Rényi entropy for z-polarized product states increases then decreases with rising initial entanglement. The first regime is driven by finite magnetization tied to local integrals of motion, while the second arises from inter-site correlations. For x- or y-polarized product states the growth instead falls monotonically. This distinction clarifies how different initial-state features control the buildup of multipartite entanglement in localized phases.","feed_headline":"MBL entanglement growth non-monotonic for z-polarized initial states","feed_subtitle":"Wehrl-Rényi entropy first rises then falls with initial entanglement due to magnetization and inter-site correlations","key_machinery":"Dynamics of the Wehrl-Rényi entropy as a multipartite-entanglement proxy, tracked under quench from structured initial states in the random-field XXZ model.","core_discovery":"The non-monotonic dependence of total entanglement entropy growth on initial entanglement, previously noted for chaotic-to-MBL quenches, also occurs in the Wehrl-Rényi entropy for z-directed product states. The first regime is governed by a finite magnetization associated with local integrals of motion, while the second reflects inter-site correlations. In contrast, product states polarized along x or y show only monotonic decay of entanglement growth.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Non-monotonic Wehrl-Renyi growth in MBL for z-polarized states","Magnetization and correlations cause non-monotonic MBL entanglement growth","Z-direction product states show two regimes in MBL Wehrl entropy","Unlike x y polarizations z states yield non-monotonic MBL entropy growth"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The random-field XXZ model at the chosen disorder strength and finite system size captures generic many-body localized behavior, and the Wehrl-Rényi entropy is an appropriate proxy for multipartite entanglement growth.","fun_headline_variants_meta":{"raw":{"variants":["Non-monotonic Wehrl-Renyi growth in MBL for z-polarized states","Magnetization and correlations cause non-monotonic MBL entanglement growth","Z-direction product states show two regimes in MBL Wehrl entropy","Unlike x y polarizations z states yield non-monotonic MBL entropy growth"]},"model":"grok-4.3","cost_usd":0.009557,"raw_usage":{"total_tokens":4186,"prompt_tokens":673,"num_sources_used":0,"completion_tokens":80,"cost_in_usd_ticks":95565500,"prompt_tokens_details":{"text_tokens":673,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3433,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":673,"tokens_out":80,"duration_ms":31607,"temperature":1.0,"reasoning_tokens":3433,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-21T05:31:30.722022+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Numerical or experimental data showing strictly monotonic Wehrl-Rényi entropy growth versus initial entanglement for z-polarized states, without the reported up-then-down behavior across a range of preparation times, would falsify the claimed two-regime structure.","supporting_citations":[],"review_version":1}