{"id":"71babb2d-1222-4ac8-9969-dc766c7e08f5","arxiv_id":"2607.06751","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"A gapless, number-conserving Luttinger liquid with short-range attraction hosts a parity-dependent edge-to-edge revival of the fermion two-point correlator, a diagnostic of Majorana edge physics.","lead":"Signatures of Majorana edge modes appear in a simple number-conserving Luttinger liquid of attractive spinless fermions, seen as a parity-dependent edge-to-edge revival of the two-point correlator. The result suggests cold-atom experiments can probe Majorana-like physics without gapped mean-field superconductors.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper's strongest claim is a concrete, falsifiable numerical statement about the two-point correlator in the number-conserving attractive t-V chain, together with its thermodynamic, parity, filling and excited-state robustness. That statement is supported by DMRG data, finite-size scaling, bosonization, and an explicit experimental protocol; the methods are standard and the manuscript is complete. The interpretive link to Majorana edge operators is imported from Ref. [13] and is the softest step, exactly as the reader notes, but the paper never claims more than \"signatures \to diagnostic,\" so the concern does not force a verdict change. An honest non-finding is therefore appropriate: no load-bearing flaw that would move the ACCEPT verdict. The suggested concrete test simply extends the existing scaling analysis away from V_c to confirm that the revival is not an artifact of proximity to phase separation.","tokens_in":16393,"tokens_out":584,"duration_ms":11304,"concrete_test":"Re-run the App. A scaling analysis of the revival max_{j\notin[1,L/2]} |⟨c†_{1} c_j⟩| for two additional interaction strengths farther from criticality (e.g., V=−1.0 and V=−0.5) at the same half-filling sequence L=4n+2; if the extrapolated L\to∞ intercept remains positive and the parity sign flip of Fig. 2b is preserved, the diagnostic is robust beyond the near-critical regime.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest-assumption note (that the parity-dependent edge-to-edge revival of ⟨c†_{1}c_L⟩ is interpreted as Majorana edge modes via the self-adjoint operators of Ref. [13], rather than a generic strong-attraction effect near V=−2) is real but does not undermine the paper's actual central claim. The claim is carefully phrased as \"signatures of Majorana edge physics\" diagnosed by the revival, not as protected topological qubits or gapped zero modes. The manuscript supplies independent numerical support that the revival is thermodynamically robust (App. A linear extrapolation to L\to∞ yields a nonzero intercept), parity-sensitive (Fig. 2b), filling-dependent with Fermi-wavelength scale (App. B), and present in low-lying excited states (bosonization modulation in App. C leaves short-distance edge physics intact). The particle-hole ansatz (Eq. 5) further shows continuous interpolation of the edge-localized coefficients \to free-fermion delocalization, consistent with the same diagnostic. No internal inconsistency or numerical red flag appears; the interpretive step is acknowledged and does not break the stated claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript studies the number-conserving attractive t-V chain of spinless fermions (Eq. 1) in the gapless Luttinger-liquid regime V > −2. Using DMRG, it shows that the ground-state two-point correlator ⟨c†₁ cⱼ⟩ decays into the bulk but revives to a finite value at the opposite edge, with a sign fixed by fermion-number parity. The revival is argued to be thermodynamically robust (Appendix A 1/L extrapolations), present at other fillings (Appendix B ΔCᵢⱼ maps), and preserved under low-lying density excitations (Appendix C bosonization). A particle-hole ansatz (Eq. 5) built from the rank-2 difference matrix ΔC interpolates continuously between edge-localized (strong-V) and free-fermion (weak-V) regimes. An ultracold-molecule/atom horseshoe geometry plus beam-splitter interferometry is proposed to measure the edge-to-edge correlator.","tokens_in":16662,"tokens_out":940,"duration_ms":10559,"significance":"If the numerical diagnostics hold, the work supplies a concrete, experimentally accessible signature of Majorana-like edge physics inside a short-range, number-conserving, gapless Luttinger liquid—outside the conventional gapped, mean-field Kitaev setting. The combination of finite-size scaling, parity dependence, filling dependence, excited-state robustness, and a simple interpolating ansatz is a solid package. The proposed cold-atom protocol (horseshoe lattice + beam-splitter occupancy) is realistic and falsifiable, and the observation that bulk correlations can be suppressed by tuning near V_c = −2 is a practical experimental advantage. These elements make the paper a useful contribution to the ongoing search for number-conserving Majorana physics.","major_comments":[{"comment":"The interpretive step that equates the parity-dependent revival of ⟨c†₁ c_L⟩ with underlying Majorana edge modes (via self-adjoint operators γ_L, γ_R satisfying P(N) = −ic ⟨N|γ_L γ_R|N⟩) is imported from Ref. [13] and is not re-derived for the short-range gapless model. While the paper carefully phrases its claim as “signatures,” a short explicit construction or numerical check of the edge operators for Eq. (1) would strengthen the central diagnostic claim and remove residual ambiguity with generic strong-attraction effects near phase separation.","section":null},{"comment":"Appendix A reports linear 1/L fits that yield nonzero intercepts (q ≈ 0.020 for V = −1.9, q ≈ 0.013 for V = −1.5). The manuscript should state the range of L used, the goodness-of-fit, and whether higher-order corrections (e.g., 1/L² or oscillatory terms) remain consistent with a finite thermodynamic limit; a single linear fit on a limited window is load-bearing for the “robust in the thermodynamic limit” claim.","section":null}],"minor_comments":[{"comment":"Fig. 2a panels for weaker V still show residual bulk oscillations; a quantitative definition of “revival magnitude” (e.g., max |⟨c†₁ cⱼ⟩| for j > L/2 minus bulk envelope) would make the V-dependence clearer.","section":null},{"comment":"Appendix C assumes continuum bosonization with periodic boundaries; a brief remark that open-boundary edge modes are not spoiled by the long-wavelength modulation would help non-specialist readers.","section":null},{"comment":"The experimental section mentions that dipolar 1/r³ interactions yield the same phenomenology; a single supplemental figure or sentence quantifying the revival for a truncated 1/r³ potential would make this claim more concrete.","section":null},{"comment":"Notation: the constant c appearing after Eq. (3) is never specified; a short definition or reference would avoid confusion.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The paper is a clean, well-executed numerical study with a realistic experimental proposal. The interpretive reliance on Ref. [13] is the only soft spot, but it does not invalidate the stated claims. Suitable for a solid condensed-matter/quantum-gas journal after the minor clarifications above."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The new result is clean: in the number-conserving attractive t-V chain (V > -2), DMRG shows that ⟨c†_{1} c_{j}⟩ decays into the bulk then revives at the opposite edge with a sign fixed by fermion parity. Appendix A extrapolates the revival to a nonzero intercept as L \to ∞; it survives other fillings (App. B) and low-lying excited states (bosonization modulation in App. C leaves the short-distance edge piece intact). The horseshoe beam-splitter protocol is concrete and matches what dipolar-molecule groups can already do.\n\nWhat they do well is keep the claim modest—“signatures of Majorana edge physics” diagnosed by the revival, not protected zero modes or a topological qubit. The particle-hole ansatz (imported from Thomas-Markarian et al.) has high overlap across a wide V range and smoothly interpolates edge-localized coefficients into free-fermion delocalization; that is useful. Methods (SyTen DMRG, standard Luttinger + bosonization) are within competence and the figures are readable.\n\nThe soft spot is exactly the one the reader flagged: equating the revival plus parity dependence with underlying Majorana operators γ_L, γ_R is taken from Ref. [13] rather than re-derived for this short-range gapless model. Near V = -2 the bulk correlations are already short-ranged, so a generic strong-attraction edge effect is not ruled out by the numerics alone. That is an interpretive risk, not a calculation error, and the paper does not over-claim protection. Citation pattern is honest; self-citation is light.\n\nThis is for people who care about number-conserving platforms and cold-atom routes to Majorana-like diagnostics. The central numerical claim is solid enough that a serious editor should send it to referees. I would bring it to reading group and would cite the revival + protocol if I were writing on related experiments.","headline":"Solid DMRG evidence for a parity-dependent edge-to-edge correlator revival in the attractive t-V Luttinger liquid, with a usable cold-atom protocol; the Majorana label is interpretive but the numerics hold.","tokens_in":17319,"tokens_out":542,"would_cite":true,"duration_ms":6536,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"In a number-conserving gapless Luttinger liquid of spinless fermions with short-range attraction, the two-point correlator revives from edge to edge with a sign fixed by fermion-number parity, giving a sharp diagnostic of Majorana edge phys","keywords":["Majorana edge modes","Luttinger liquid","number-conserving models","attractive interactions","two-point correlator revival","ultracold dipolar gases","beam-splitter interferometry","particle-hole ansatz"],"falsifier":"Measure or compute the two-point correlator ⟨c†_1 c_L⟩ (or ⟨c†_d c_{L+1-d}⟩) on large open chains of the attractive t-V model at fixed filling as V approaches -2 from above; if the edge revival vanishes in the thermodynamic limit or loses its strict parity dependence, the claimed Majorana diagnostic fails.","tokens_in":17215,"feed_emoji":"⚛️","tokens_out":863,"duration_ms":7443,"temperature":0.7,"pith_summary":"Majorana edge modes are usually discussed in gapped, particle-number-nonconserving models such as the Kitaev chain. This paper claims that clear signatures of the same edge physics survive in the conceptually simplest number-conserving, gapless setting: a one-dimensional chain of spinless fermions with nearest-neighbor attraction, still inside the Luttinger-liquid phase. The diagnostic is ordinary two-point correlators: when one operator sits at one edge, the correlator decays into the bulk yet revives to a finite value at the opposite edge; the sign of that revival flips with the parity of the total fermion number. The revival remains finite in the thermodynamic limit, appears at other fillings, and is still present in low-lying excited states. A simple particle-hole ansatz that relates the even- and odd-parity ground states works across a wide range of interaction strengths, interpolating between free fermions and a strongly interacting Majorana regime. Because the model is number-conserving and can be realized with dipolar atoms or molecules, the authors also sketch a beam-splitter interferometry protocol that would measure the edge-to-edge correlator directly.","feed_headline":"Edge-to-edge correlator revival signals Majorana physics","feed_subtitle":"Even in a gapless, number-conserving Luttinger liquid the revival tracks fermion parity and survives the thermodynamic limit","key_machinery":"The edge-to-edge revival of the normal two-point correlator ⟨c†_1 c_j⟩ (and of ⟨c†_d c_{L+1-d}⟩), whose sign tracks fermion parity. This is interpreted, via a particle-hole ansatz for the odd-parity ground state, as the number-conserving analogue of the non-local Majorana bilinear that encodes parity in the Kitaev chain.","core_discovery":"Signatures of Majorana edge physics persist in a number-conserving, gapless Luttinger liquid of spinless fermions with short-range attractive interactions. The two-point correlator evaluated on the ground state (and on low-lying excited states) decays into the bulk but revives at the opposite edge with a sign fixed by fermion-number parity; the revival is thermodynamically robust and is captured by a particle-hole ansatz that interpolates between free-fermion and strongly interacting limits.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Parity-signed edge revival marks Majorana in gapless Luttinger liquid","Majorana edge physics survives in number-conserving Luttinger liquid","Edge correlator revives with fermion parity in attractive Luttinger liquid","Gapless attractive Luttinger liquid hosts robust Majorana edge revival","Two-point correlator tracks Majorana parity across Luttinger edges"],"cache_read_input_tokens":128,"weakest_assumption_plain":"That a finite, parity-dependent edge-to-edge revival of the ordinary two-point correlator is enough, by itself, to identify underlying Majorana edge modes rather than a generic correlation effect of strong attraction near the phase-separation point.","fun_headline_variants_meta":{"raw":{"variants":["Parity-signed edge revival marks Majorana in gapless Luttinger liquid","Majorana edge physics survives in number-conserving Luttinger liquid","Edge correlator revives with fermion parity in attractive Luttinger liquid","Gapless attractive Luttinger liquid hosts robust Majorana edge revival","Two-point correlator tracks Majorana parity across Luttinger edges"]},"model":"grok-4.5","effort":"low","cost_usd":0.003276,"raw_usage":{"total_tokens":1160,"prompt_tokens":825,"num_sources_used":0,"completion_tokens":79,"cost_in_usd_ticks":32760000,"prompt_tokens_details":{"text_tokens":825,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":256,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":825,"tokens_out":79,"duration_ms":3998,"temperature":1.0,"reasoning_tokens":256,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T22:03:52.853058+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure or compute the two-point correlator ⟨c†_1 c_L⟩ (or ⟨c†_d c_{L+1-d}⟩) on large open chains of the attractive t-V model at fixed filling as V approaches -2 from above; if the edge revival vanishes in the thermodynamic limit or loses its strict parity dependence, the claimed Majorana diagnostic fails.","supporting_citations":[],"review_version":1}