{"id":"7466d164-93bf-4afc-91c9-d6e3b158574d","arxiv_id":"2608.09304","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"During a holographic global quench, multipartite entanglement's spatial range first expands then contracts, with higher-party entanglement relaxing later, while some tripartite signals persist or return to vacuum values.","lead":"This paper computes how multipartite entanglement, not just ordinary two-party entanglement, evolves when a strongly coupled quantum system is suddenly energized and then settles to thermal equilibrium. It finds that collective entanglement first spreads over larger separations, then shrinks, and that more-party entanglement relaxes more slowly.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified to the central HEGMEC dynamics claim.","rationale":"The reader's weakest_assumption targets the Section 5 genuine tripartite multi-entropy result, which is not part of the strongest_claim about HEGMEC critical separations and integrated multipartite signals. I agree that the conjectural covariant soap-film prescription and the Section 3.4 placeholders justify a CONDITIONAL overall verdict, but they are not load-bearing for the central HEGMEC claim. That claim is supported by a well-posed numerical procedure built on analytic HRT geodesic lengths, and the key ordering properties are checked in the displayed curves. The only way the central claim could fail is through a numerical implementation error, hence the proposed independent reproduction check is the appropriate test.","tokens_in":27577,"tokens_out":45719,"duration_ms":484385,"concrete_test":"Reproduce Figure 2 by independently implementing the HRT geodesic length in (A.17) and solving I_n(l,d,t)=0 for r_H=1 and l=1,2,3,4,5,10 with an independent root-finder; then recompute E_n(t) by numerical quadrature over the HEGMEC windows. Confirm that every d_n(l,t) curve has a single maximum, that d_{n-1}(l,t)<d_n(l,t) holds at all times, and that the peak times of E_n(t) are strictly ordered by n. If the ordering or peak hierarchy is not reproduced, the central claim would need revision.","verdict_should_be":"UNCHANGED","load_bearing_attack":"I read the central claim as the HEGMEC-based results in Section 3.3: the critical separations d_n(l,t) are nonmonotonic with a single maximum, and the integrated signals E_n(t) peak later for larger n. The derivation is internally consistent: the geodesic lengths in (A.17) are the standard thin-shell HRT results; I_n=0 in the HEGMEC window is equivalent to the connected/disconnected degeneracy of the full n-union; the ordering d_{n-1}<d_n is verified numerically; and the late-time plateau d_f=log2/r_H follows from equations (3.31)-(3.34). I find no algebraic or conceptual error in the steps supporting this claim. The paper's own limitations are real but local: the unresolved '(??)' placeholders in Section 3.4 block checking the upper-bound-deficit derivation, and the Section 5 GM(3) vacuum-return result rests on the conjectural covariant soap-film prescription. Neither affects the central HEGMEC dynamics claim itself, though both justify keeping the overall verdict conditional.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies multipartite entanglement dynamics in AdS3-Vaidya after a global quench. Using the standard HRT geodesic formulas, it constructs holographic exclusive global multipartite entanglement configurations (HEGMECs) for n=2,...,6, computes the critical separations d_n(l,t) at which n-interval entanglement wedges connect, and defines integrated signal strengths E_n(t) over the HEGMEC windows. The paper reports that the spatial range of multipartite entanglement first expands and then contracts, with E_n(t) peaking later for larger n. It also computes the Markov gap in Section 4 and the genuine tripartite multi-entropy in Section 5, finding that the Markov gap can remain enhanced after local thermalization while GM^(3) returns to its vacuum value for the adjacent tripartition. Section 3.4 compares the optimized upper bound of -I3 in the late-time pure Vaidya state and in a thermal BTZ state, deriving a finite deficit DeltaU(l) whose critical length coincides with the thermal screening scale d_f=ln2/r_H.","tokens_in":27754,"tokens_out":9697,"duration_ms":99061,"significance":"If the results hold, this is a valuable and quantitative step beyond bipartite entanglement probes of holographic thermalization: it gives concrete, parameter-free predictions for the evolution of multipartite spatial ranges and integrated signals. The central HEGMEC analysis is internally consistent: it uses standard thin-shell HRT geodesic lengths, the connected/disconnected degeneracy of the full n-union determines d_n, the ordering d_{n-1}<d_n is checked numerically, and the late-time plateau d_f=log2/r_H follows analytically from Eqs. (3.31)-(3.34). No constants are fitted; r_H=1 is a scale choice. The paper is also candid about the conjectural status of the covariant soap-film prescription used in Section 5, which is an honest limitation. The work is likely to be of interest to the JHEP readership working on holographic entanglement and thermalization.","major_comments":[{"comment":"The derivation of DeltaU(l) contains unresolved placeholders: the text reads 'Using (??) and (3.56)' and 'the first RT branch in (??) dominates'. These prevent the reader from verifying how Eq. (3.58) and the branch threshold l_c=ln2 in Eq. (3.59) are obtained from the preceding I_th(A:B) expression and the definition of U_th(l). Because the identity l_c=d_f is advertised as one of the paper's results, these cross-references must be completed and the branch argument spelled out. This is a load-bearing gap in Section 3.4, even though it does not affect the Section 3.3 HEGMEC curves.","section":"3.4, after Eq. (3.56)"},{"comment":"The late-time result GM^(3)_final = GM^(3)_vac is obtained by applying the 'proposed' covariant soap-film prescription of [28] to the time-dependent Vaidya geometry, as the paper itself flags on page 31. If that prescription is not valid or requires corrections in this background, the nonmonotonic evolution in Figure 10 and the vacuum-return statement in Eq. (5.20) do not follow. The authors should either supply supporting evidence for the covariant prescription (for example, consistency checks in the static BTZ limit, branch selection rules, or a discussion of why the extremal network is the correct one) or explicitly qualify the abstract and conclusions so that this result is presented as conditional on the conjecture.","section":"5, Eq. (5.3) and (5.20)"}],"minor_comments":[{"comment":"The definition of E_n(t) sums over indices 1<=i_1<...<i_n<=N, but N is not specified in the text; since the boundary is noncompact, please state explicitly that a finite chain of N intervals is considered and define N before the formula.","section":"3.3.2, Eq. (3.38)"},{"comment":"The two branches of I_th(A:B) are presented after taking the L0 to infinity limit; showing the finite-L0 expression or a short derivation would make the branch competition in Eq. (3.56) more transparent.","section":"3.4, Eq. (3.54)"},{"comment":"The partition has C=A union B, which is noncompact; please specify the regulator and UV subtraction used for the multi-entropy and for GM^(3) so that the finite quantity in Eq. (5.14) is unambiguous.","section":"5, Eq. (5.4)"},{"comment":"The phrase 'thermal-form entropy' is awkward and unclear; it should likely read 'thermal-state entropy' or 'thermal-form entanglement entropy'.","section":"4, last paragraph"},{"comment":"The finite-l correction in Eq. (3.35) is stated without derivation; a brief footnote showing the expansion of Eq. (3.31) would help the reader verify the claimed 1/(n-1) prefactor.","section":"3.3.1, item III"},{"comment":"The quantity s(ell,t_b) is used in Eq. (2.12) before it is defined; either define it in the main text or add an explicit pointer to Appendix A where it is introduced.","section":"2.2, Eq. (2.12)"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Ju et al. compute the time-dependent HEGMEC critical separations, integrated n-partite signals, Markov gap, and genuine tripartite multi-entropy for the AdS3-Vaidya global quench. The central claim—that d_n(l,t) grows then shrinks, and that higher-n integrated signals peak later—is new and, as far as I can tell, correct. The methods are standard HRT geodesics from Balasubramanian et al., the numerics are straightforward, and there are no fitted parameters: r_H is just a scale choice. The paper is honest about what is conjectural. The Section 5 multi-entropy result explicitly relies on the proposed covariant soap-film prescription from [28], so the late-time vacuum-return of GM^(3) is conditional on that conjecture holding in Vaidya. The authors flag that. Likewise, the l_c = d_f coincidence is a clean result that the paper derives rather than assumes. I agree with the stress-test: I find no algebraic error in the Section 3.3 derivation.\n\nThe soft spots are local but real. Section 3.4 contains literal '(??)' placeholders around Eqs. (3.56)-(3.59). That blocks checking the upper-bound deficit derivation. It looks like a leftover from manuscript preparation, but for arXiv and JHEP it is not acceptable. Also, the integrated E_n definition integrates J_n over d, but the general-n dependence of the integrand is not spelled out; only n=2,3 formulas are explicit. Minor: the claim that the Markov gap 'can remain enhanced after local thermalization' is specific to the d range considered; not a flaw, just a boundary condition.\n\nThe paper is a subfield contribution, not a revolution. It extends the known bipartite tsunami picture to higher-party structure. For a reader working on holographic entanglement dynamics or multipartite entanglement in AdS/CFT, this is worth citing. I would not desk-reject it. Send it to a competent referee; the placeholders should be fixed before acceptance. If the authors fix the placeholders and keep the conjecture caveat explicit, conditional acceptance is reasonable.","headline":"A solid, genuinely new computation of multipartite entanglement dynamics in AdS3-Vaidya, with a few presentational holes that a referee can fix.","tokens_in":28303,"tokens_out":2030,"would_cite":true,"duration_ms":21263,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that a global quench in the AdS3-Vaidya holographic setting rearranges multipartite entanglement so that its spatial range first expands, then contracts, with larger-$n$ signals peaking later.","keywords":["multipartite entanglement","holographic thermalization","AdS3-Vaidya","n-partite information","HEGMEC","Markov gap","multi-entropy","entanglement wedge"],"falsifier":"Compute the genuine tripartite multi-entropy for the same adjacent-interval partition in a two-dimensional CFT global quench using an independent replica or lattice method; if the late-time value differs from $c/2\\,\\log(2/\\sqrt3)$, the soap-film-based prediction fails. Alternatively, run a tensor-network simulation of a 1D critical chain after a global quench and check whether the Markov gap late-time plateau exceeds the vacuum value for small separations.","tokens_in":27374,"feed_emoji":"🕸️","tokens_out":7454,"duration_ms":70921,"temperature":0.7,"pith_summary":"The paper claims that a global quantum quench in a two-dimensional holographic CFT reorganizes multipartite entanglement in a specific, time-ordered way: the spatial range over which $n$ intervals share a connected entanglement wedge first expands, then contracts as the system approaches local thermal equilibrium. Using the AdS$_3$-Vaidya dual, the authors compute critical separations $d_n(l,t)$ for $n=2,\\dots,6$ and integrated HEGMEC signals $E_n(t)$, finding that all connectivity ranges grow on comparable early-time scales but relax hierarchically, with larger-$n$ signals peaking later and decaying more slowly. They also find that the Markov gap can remain enhanced after local thermalization, while the genuine tripartite multi-entropy for adjacent intervals returns to its vacuum value. These results matter because they show that thermalization redistributes entanglement across both spatial scales and multipartite structure, not just entropy magnitude.","feed_headline":"Multipartite entanglement spreads, then retreats after a quench","feed_subtitle":"n-party correlations peak later for larger n and relax slower as 2D holographic thermalization proceeds.","key_machinery":"The argument runs on the AdS$_3$-Vaidya thin-shell geometry. Boundary-anchored HRT geodesics are matched across the null shell; the renormalized length $L_{\\rm ren}(\\ell,t_b)$ in equation (2.12) supplies every entropy input. For $n$ equal intervals, the authors classify admissible non-crossing pairings; the dominant pairing defines the entanglement-wedge connectivity, and the HEGMEC window $d_{n-1}(l,t)<d<d_n(l,t)$ isolates exclusive $n$-partite entanglement. The critical curves $d_n(l,t)$ are solved numerically from $I_n(l,d_n,t)=0$; the integrated strength $E_n(t)$ then sums $J_n=(-1)^n I_n$ over the window. The Markov gap uses the entanglement-wedge cross-section $E_W$ via $h=2E_W-I(A:B)$, and the genuine tripartite multi-entropy uses a conjectured covariant three-leg soap-film network whose length $\\Gamma(t)$ is extremized over a bulk junction.","core_discovery":"The central discovery is that after a global quench in AdS$_3$-Vaidya, the reach of irreducible multipartite entanglement is transient: for equal intervals of length $l$, the critical separations $d_n(l,t)$ marking the transition between connected and disconnected $n$-party entanglement wedges rise above their vacuum values, peak near $t\\simeq l/2$, and then fall to a common late-time plateau $d_f=\\log 2/r_H$ for large $l$. In a fixed spatial configuration, the decreasing curves are crossed in order of increasing $n$, so the minimal number of intervals needed to support a connected wedge grows with time: the surviving collective entanglement migrates to larger total spatial separations. The integrated signal $E_n(t)$ peaks later for larger $n$, and the Markov gap can stay above its vacuum value after local thermalization, whereas the genuine tripartite multi-entropy $GM^{(3)}$ returns exactly to its vacuum value for the adjacent tripartition. The paper presents this as evidence that global quenches propagate entanglement from shorter to longer scales while reorganizing its multipartite structure.","pith_inferences":["The peak-time ordering $t_{n,\\max}^{(E)} > t_{n-1,\\max}^{(E)}$ might be a generic diagnostic of multipartite entanglement propagation in any quantum quench with a light cone, independent of holography; a tensor-network or cold-atom experiment could test it.","The coincidence $l_c = d_f = \\log 2/r_H$ suggests a single thermal scale governs both the onset of correlations with an external purifier and the loss of same-boundary wedge connectivity; one could test whether this equality survives in higher-dimensional or charged Vaidya geometries, where BTZ-specific formulas change.","The re-entrant Markov-gap dynamics (zero-positive-zero for fixed separation $d$ with $d_2(0)<d<d_{2,\\max}$) predicts a transient window where reflected entropy exceeds mutual information; this is a sharp, falsifiable signature for numerical simulations.","The HEGMEC-isolation idea could be checked in non-holographic quenches by comparing $(-1)^n I_n$ inside and outside the window in random stabilizer or free-fermion systems, testing whether fewer-party contributions indeed vanish."],"forward_implications":["When the critical curves $d_n(l,t)$ cross a fixed separation in descending order, the minimal collective support for a connected wedge grows from few intervals to many: surviving multipartite entanglement is carried by structures spanning larger spatial distances.","Because $E_n(t)$ peaks later for larger $n$, the integrated multipartite signal remains dynamically active after two-party entanglement has saturated, so local entropy saturation does not signal the end of multipartite reorganization.","The late-time plateau $d_{n,f}\\simeq \\log 2/r_H$ independent of $n$ for large $l$ implies thermal screening compresses all connectivity ranges to a single temperature-determined scale.","The Markov gap remaining above its vacuum value after local thermalization means the locally thermal pure state is less reducible to a triangle or SOTS structure than the vacuum for the same subregions.","The genuine tripartite multi-entropy returning to vacuum shows that the quench leaves no residual $GM^{(3)}$ for the adjacent partition, even though the state's entanglement structure is not identical to the vacuum."],"supporting_citations":[{"why":"Supplies the analytic thin-shell HRT geodesic lengths (2.12) used in every entropy combination.","marker":"[8]"},{"why":"Establishes the non-monotonic time evolution of mutual and tripartite information in AdS-Vaidya that this paper extends to higher n.","marker":"[10]"},{"why":"Provides the earlier extension to holographic n-partite information for strip configurations, the baseline for I_4 and I_5 behavior.","marker":"[19]"},{"why":"Defines HEGMECs and the upper-bound configuration logic that justifies treating (-1)^n I_n as exclusive n-partite entanglement.","marker":"[21]"},{"why":"Provides the general upper bound of -I_3 used in the purification comparison of Section 3.4.","marker":"[22]"},{"why":"Introduces the reflected entropy whose difference from mutual information defines the Markov gap.","marker":"[24]"},{"why":"Develops the Markov gap for geometric reflected entropy and its interpretation as a tripartite-structure diagnostic.","marker":"[25]"},{"why":"Proposes the multi-entropy soap-film prescription (static and covariant) on which the GM(3) calculation depends.","marker":"[28]"},{"why":"Defines genuine tripartite multi-entropy GM(3) by subtracting bipartite contributions from S^(3).","marker":"[29]"},{"why":"Supplies the three-branch time-dependent entanglement-wedge cross-section in Vaidya used to evaluate the Markov gap.","marker":"[43]"}],"fun_headline_variants":["Quench: multipartite entanglement spreads then contracts","Entanglement wave expands and contracts after a quench","Multipartite entanglement peaks mid-quench, then retreats","Later peaks, slower relaxation in n-party entanglement after quench","Holographic quench reorganizes multipartite entanglement"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The late-time result for the genuine tripartite multi-entropy depends on a still-unproven guess about how to compute that quantity in changing spacetimes; if the guess is wrong, that result falls.","fun_headline_variants_meta":{"raw":{"variants":["Quench: multipartite entanglement spreads then contracts","Entanglement wave expands and contracts after a quench","Multipartite entanglement peaks mid-quench, then retreats","Later peaks, slower relaxation in n-party entanglement after quench","Holographic quench reorganizes multipartite entanglement"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000725,"raw_usage":{"total_tokens":3271,"prompt_tokens":987,"completion_tokens":2284,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":603,"completion_tokens_details":{"reasoning_tokens":2203}},"tokens_in":603,"tokens_out":2284,"duration_ms":17467,"temperature":1.0,"reasoning_tokens":2203,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T19:42:32.867870+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the genuine tripartite multi-entropy for the same adjacent-interval partition in a two-dimensional CFT global quench using an independent replica or lattice method; if the late-time value differs from $c/2\\,\\log(2/\\sqrt3)$, the soap-film-based prediction fails. Alternatively, run a tensor-network simulation of a 1D critical chain after a global quench and check whether the Markov gap late-time plateau exceeds the vacuum value for small separations.","supporting_citations":[{"cited_title":"On the Time Evolution of Holographic n-partite Information","cited_arxiv_id":"1406.7677","evidence_quote":"Provides the earlier extension to holographic n-partite information for strip configurations, the baseline for I_4 and I_5 behavior."},{"cited_title":"Evolution of Entanglement Wedge Cross Section Following a Global Quench","cited_arxiv_id":"2005.05673","evidence_quote":"Supplies the three-branch time-dependent entanglement-wedge cross-section in Vaidya used to evaluate the Markov gap."}],"review_version":1}