{"id":"1aae70ae-f5b9-430d-9ac6-9dea065a2afb","arxiv_id":"2606.05757","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Multipartite entanglement quantities in holographic Weyl semimetals develop features at the topological critical point and distinguish phases through anisotropic large-l scaling.","lead":"This paper computes multipartite entanglement measures such as conditional mutual information and entanglement wedge cross sections in a holographic model of Weyl semimetals. These quantities show distinct features at the topological transition and differ by direction in the nontrivial phase.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Holographic dictionary for multipartite measures (multi-EWCS, Markov gap, κ) rests on conjectures whose validity is assumed rather than verified for this geometry","rationale":"The reader's weakest assumption is exactly the load-bearing step; the full text supplies the numerical implementation but does not add independent evidence for the multipartite dictionary, leaving the UNVERDICTED verdict appropriate.","tokens_in":1742,"tokens_out":339,"duration_ms":16234,"concrete_test":"Take the pure AdS_{5} limit of the same strip geometry, compute the same multi-EWCS and Δ quantities numerically with the code used in the paper, and compare to the exact CFT_{4} results for tripartite information and entanglement of purification on strips; agreement to within 5 % would support the dictionary for this class of models.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that tripartite/four-partite quantities develop diagnostic features at the critical point and distinguish anisotropic IR phases. This requires that the bulk geometric constructions (EWCS, multi-EWCS, etc.) equal the corresponding field-theory entanglement quantities. While the Ryu-Takayanagi formula for EE is standard, the identifications for conditional mutual information, Markov gap, and multi-EWCS are proposals (e.g., EWCS \to EoP). The paper computes these in the numerical holographic Weyl-semimetal background but supplies no cross-check against a solvable limit or independent field-theory computation, so the mapping remains an untested premise for the diagnostic power asserted at large but finite l.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript examines multipartite entanglement structures in the zero-temperature holographic Weyl semimetal. For strip regions it computes conditional mutual information, the entanglement wedge cross section, tripartite measures κ and the Markov gap, multi-EWCS, and the four-partite signals Δ and g as functions of strip width l and the tuning parameter across the topological transition. At fixed large l these quantities develop features near the critical point; their large-l anisotropic behavior is reported to distinguish the nontrivial phase from the trivial phase, with the l-dependence governed by the IR scaling of the geometry.","tokens_in":1877,"tokens_out":369,"duration_ms":24889,"significance":"If the mappings hold, the work demonstrates that tripartite and four-partite holographic entanglement quantities can serve as nonlocal diagnostics for topological phase transitions and IR anisotropy, extending the reach of entanglement probes beyond bipartite measures in a strongly coupled condensed-matter model. The direct use of the numerical bulk geometry to extract power-law IR scaling is a concrete strength.","major_comments":[{"comment":"The central claim that the computed geometric quantities diagnose the topological transition and distinguish anisotropic phases rests on the identification of multi-EWCS, the Markov gap, κ, Δ and g with the corresponding field-theory multipartite entanglement measures. These identifications are proposals (EWCS → EoP and extensions to multipartite cases) rather than theorems verified for the present background; the manuscript supplies no cross-check against a solvable limit or independent field-theory computation. This assumption is load-bearing for the diagnostic power asserted at large but finite l.","section":"Sections defining the multipartite quantities and the numerical results"}],"minor_comments":[],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading of the manuscript and for highlighting both its potential significance and the need for precision regarding the conjectural status of the entanglement mappings. We respond to the major comment below.","responses":[{"response":"We agree that the identifications of multi-EWCS, the Markov gap, κ, Δ and g with field-theory multipartite entanglement measures rest on conjectural proposals extending the EWCS-EoP relation, rather than on theorems proven for this background. The manuscript contains no independent cross-checks against solvable limits or direct field-theory computations, which is a limitation of the present holographic setup. Within the holographic framework, however, these geometric quantities are computed directly from the bulk metric and are shown to develop clear features near the critical point at fixed large l and to exhibit anisotropic power-law scaling governed by the IR geometry; these behaviors are independent of the precise field-theory interpretation. In the revised manuscript we will add explicit caveats in the introduction, the sections defining the quantities, and the conclusions, stating the conjectural nature of the mappings and restricting the diagnostic claims to the holographic quantities themselves.","revision_made":"yes","referee_comment":"[Sections defining the multipartite quantities and the numerical results] The central claim that the computed geometric quantities diagnose the topological transition and distinguish anisotropic phases rests on the identification of multi-EWCS, the Markov gap, κ, Δ and g with the corresponding field-theory multipartite entanglement measures. These identifications are proposals (EWCS → EoP and extensions to multipartite cases) rather than theorems verified for the present background; the manuscript supplies no cross-check against a solvable limit or independent field-theory computation. This assumption is load-bearing for the diagnostic power asserted at large but finite l."}],"tokens_in":1323,"tokens_out":376,"duration_ms":19486,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that conditional mutual information, the Markov gap, multi-EWCS, and the derived four-partite signals all develop clear features near the critical point at fixed large strip width, and their large-l directional dependence separates the two phases.\n\nThe work applies these measures systematically to strip regions in the numerical holographic background, tracks their power-law IR scaling set by the geometry, and checks both the transition and the anisotropy. That consistent treatment across several quantities and orientations is the concrete advance.\n\nThe calculations look internally consistent within the holographic setup. The authors vary the tuning parameter and strip direction in a controlled way and report the expected IR behavior.\n\nThe soft spot is the dictionary. Ryu-Takayanagi for ordinary entanglement is standard, but the identifications for conditional mutual information, Markov gap, and multi-EWCS rest on proposals that have not been cross-checked in this anisotropic geometry or against an independent field-theory calculation. Without that, the diagnostic claim at large but finite l remains plausible rather than verified.\n\nThis is for people already working on holographic condensed-matter models who use entanglement as a probe. A reader who wants to see how multipartite measures behave in a model with both topology and anisotropy will get usable results. It deserves a serious referee because the numerics are nontrivial and the claims are specific enough to be tested.","headline":"The paper shows multipartite entanglement quantities flag the topological transition and anisotropy in the holographic Weyl semimetal, but the bulk-to-field-theory mapping for those quantities stays conjectural.","tokens_in":2398,"tokens_out":353,"would_cite":false,"duration_ms":16001,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Tripartite and four-partite entanglement structures diagnose the topological phase transition in holographic Weyl semimetals.","keywords":["holographic Weyl semimetal","multipartite entanglement","topological phase transition","anisotropy","entanglement wedge cross section","conditional mutual information","Markov gap"],"falsifier":"Direct computation of the same multipartite entanglement quantities in the dual field theory that shows no clear features near the critical point at fixed large l.","tokens_in":2620,"feed_emoji":"🔬","tokens_out":635,"duration_ms":22197,"temperature":0.7,"pith_summary":"The paper computes multipartite entanglement quantities such as conditional mutual information, entanglement wedge cross section, tripartite measures κ and Markov gap, and four-partite signals Δ and g for strip regions in a holographic Weyl semimetal model. These quantities are tracked as functions of strip width l and the tuning parameter that drives the topological transition. At fixed large l, all quantities develop clear features near the critical point, and their large-l scaling is anisotropic in the nontrivial phase. A sympathetic reader would care because this offers a nonlocal entanglement-based way to identify topological transitions and IR anisotropy without local order parameters.","feed_headline":"Multipartite entanglement detects topological transitions","feed_subtitle":"Tripartite and four-partite measures show clear signatures at the critical point and distinguish phases via anisotropic large-l scaling.","key_machinery":"Multipartite entanglement quantities (conditional mutual information, EWCS, κ, Markov gap, multi-EWCS, and four-partite signals Δ and g) computed geometrically in the holographic bulk for strip regions.","core_discovery":"In the zero-temperature holographic Weyl semimetal, tripartite and four-partite entanglement quantities for strip regions develop clear features near the critical point at fixed large l, showing that these structures diagnose the topological quantum phase transition. At large l their dependence on l takes a power-law form governed by the IR scaling of the system. Anisotropic large-l behavior in different directions distinguishes the nontrivial phase from the trivial phase.","pith_inferences":["The same geometric method could be applied to other holographic models of topological materials to check whether multipartite entanglement remains diagnostic.","If the duality holds, field-theory calculations or quantum simulations of the dual theory should reproduce the reported features at the critical point.","Direction-dependent entanglement measures might suggest protocols for detecting anisotropy in real condensed-matter Weyl semimetals."],"forward_implications":["Tripartite and four-partite entanglement structures diagnose the topological quantum phase transition.","Anisotropic large-l behavior distinguishes the nontrivial phase from the trivial phase.","At large l the quantities follow power-law forms set by the IR scaling.","Multipartite holographic entanglement serves as a sensitive nonlocal probe of topological transitions and anisotropic IR physics."],"fun_headline_variants":["Multipartite entanglement detects Weyl semimetal transitions","Tripartite measures probe topological phase transitions","Entanglement quantities reveal anisotropy in Weyl semimetals","Holographic entanglement diagnoses phase transitions and anisotropy","Large l entanglement scaling signals nontrivial Weyl phases"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The holographic model and its geometric entanglement calculations accurately reproduce the entanglement structure of the dual field theory.","fun_headline_variants_meta":{"raw":{"variants":["Multipartite entanglement detects Weyl semimetal transitions","Tripartite measures probe topological phase transitions","Entanglement quantities reveal anisotropy in Weyl semimetals","Holographic entanglement diagnoses phase transitions and anisotropy","Large l entanglement scaling signals nontrivial Weyl phases"]},"model":"grok-4.3","cost_usd":0.00693,"raw_usage":{"total_tokens":3202,"prompt_tokens":645,"num_sources_used":0,"completion_tokens":67,"cost_in_usd_ticks":69299500,"prompt_tokens_details":{"text_tokens":645,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2490,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":645,"tokens_out":67,"duration_ms":18011,"temperature":1.0,"reasoning_tokens":2490,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T00:25:30.915002+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct computation of the same multipartite entanglement quantities in the dual field theory that shows no clear features near the critical point at fixed large l.","supporting_citations":[],"review_version":1}