{"id":"3d045c97-33d4-49e5-99e0-42b7fbdd6af9","arxiv_id":"2505.02661","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In a long-range Ising chain, noiseless ramps still produce defects scaling as tau_Q^(-1/2), while white noise makes defects increase with ramp time and suppresses the enhancement from longer-range interactions.","lead":"This paper calculates how defects form when a long-range Ising magnet is driven slowly across two phase transitions, with and without classical noise. It finds the noiseless Kibble-Zurek exponent survives, while noise shifts the dominant fluctuation modes toward small momentum and weakens defect production as interactions become more long-ranged.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (A2)'s expansion of f∞α near k=π is wrong: the coefficient is η(α−1)/ζ(α), not ζ(1−α)/ζ(α), so the dominant noiseless defect-density prefactor and correlation lengths are quantitatively incorrect.","rationale":"The paper's central noiseless claim is that defect density scales as n∝τ_Q^{-1/2} with a prefactor B(α) that grows as α decreases, and this same k=π contribution drives the noise-suppression term in Eq. (17). The expansion coefficient at k=π is therefore load-bearing, even though the scaling exponent itself is robust. The direct summation test shows that Eq. (A2) has the wrong coefficient: the paper's ζ(1−α)/ζ(α) is neither the correct η(α−1)/ζ(α) nor the ζ(α−1)/ζ(α) that appears in Eq. (11). This internal inconsistency means the analytic prefactors, correlation lengths, and the quantitative α-dependence of the defect density are not trustworthy, even if the qualitative direction of the α-dependence survives. The reader's stated weakest assumption was the white-noise approximation in the noisy sector, which is a separate regime limitation; the reader did note the k=π expansion as questionable in the rationale, so my concern partially agrees. Because the error affects quantitative accuracy rather than the main scaling law, the existing CONDITIONAL verdict remains appropriate: the paper should be accepted only after the expansion coefficient is corrected and the derived prefactors are recomputed.","tokens_in":19578,"tokens_out":25464,"duration_ms":296587,"concrete_test":"Directly evaluate f∞α(π−δ) numerically for α=1.5, δ=0.1 using the defining sum (1/ζ(α))Σ_{r=1}^{10000}(−1)^{r+1} sin(rδ)/r^α, or equivalently the polylog expression −Im Liα(−e^{iδ})/ζ(α). Compare the result with Eq. (A2) and with [η(α−1)/ζ(α)]δ. If the numerical value matches Eq. (A2), the paper stands; if it matches the η-form, then Eq. (A2), B(α) in Eq. (12), and ξ0 in Eq. (19) require correction before any quantitative use.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Appendix A, the expansion of f∞α(k) near k=π is incorrect. Writing k=π−δ, f∞α(k)=(1/ζ(α))Σ_r sin(r(π−δ))/r^α=(1/ζ(α))Σ_r(−1)^{r+1} sin(rδ)/r^α ≈ [η(α−1)/ζ(α)]δ, with η(s)=(1−2^{1−s})ζ(s). The stated Eq. (A2) gives [ζ(1−α)/ζ(α)]δ, which has the wrong sign and magnitude (e.g. α=1.5: −0.0796 vs +0.2316). Moreover Eq. (11) uses φ∝[ζ(α−1)/ζ(α)]^2, which is neither the coefficient of (A2) nor the correct η(α−1)/ζ(α). Since the k=π region is the dominant source of noiseless defects for 1<α<2, the prefactor B(α) in Eq. (12), the correlation length ξ0=√(4φτQ), and the noisy suppression term in Eq. (17) all inherit this quantitative error. The τ_Q^{-1/2} exponent is unaffected because the functional form f∝δ is correct, but the α-dependence of defect densities and correlation lengths is not reliable.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a one-dimensional long-range transverse-field Ising chain driven linearly across two quantum critical points, with and without time-dependent noise. Using a Jordan-Wigner mapping and a Landau-Zener description, the authors derive approximate analytic expressions for the defect density, two-point and spin correlation functions, and the full counting statistics of defects as functions of the quench time tau_Q, the interaction decay exponent alpha, and the noise strength. The central noiseless claim is the Kibble-Zurek scaling n proportional to tau_Q^{-1/2} with an alpha-dependent prefactor that increases as alpha decreases; in the noisy case the paper reports anti-Kibble-Zurek behavior with suppression as alpha decreases, Gaussian-to-quadratic crossover in fermionic correlators, exponential decay of spin correlators, and near-Gaussian kink statistics.","tokens_in":19816,"tokens_out":23925,"duration_ms":272542,"significance":"The topic is timely: extending Kibble-Zurek and anti-Kibble-Zurek phenomenology to long-range interacting systems is of active interest, and the paper provides an exactly solvable free-fermion setting with closed-form Landau-Zener and full-counting-statistics formulas. The derivations are analytic and contain no fitted free parameters, which is a genuine strength. However, the quantitative alpha-dependent statements rest on a polylogarithm expansion in Appendix A that is incorrect, and the noisy results inherit that error through the expansion of f_alpha(k). The n proportional to tau_Q^{-1/2} exponent and the Gaussian/exponential forms of the correlations are likely robust, but the alpha-dependent prefactors, correlation lengths, and the reported suppression magnitudes need to be recomputed before the main conclusions can be trusted.","major_comments":[{"comment":"The small-delta expansion of f_inf_alpha(k) near k=pi is incorrect. Since f_inf_alpha(k) = zeta(alpha)^{-1} sum_r r^{-alpha} sin(rk), writing k=pi-delta gives f_inf_alpha(pi-delta) = [eta(alpha-1)/zeta(alpha)] delta + O(delta^3), with eta(s) = (1 - 2^{1-s}) zeta(s). For alpha=1.5 the correct coefficient is +0.232, whereas Eq. (A2) gives zeta(1-alpha)/zeta(alpha) = -0.080. Moreover, Eq. (11) defines phi(alpha)=pi[zeta(alpha-1)/zeta(alpha)]^2, which is neither the coefficient from Eq. (A2) nor the correct coefficient; the correct phi is pi[eta(alpha-1)/zeta(alpha)]^2 = (1-2^{2-alpha})^2 times the stated value. This error propagates into the prefactor B(alpha) in Eq. (12), the correlation length xi_0 = sqrt(4 phi tau_Q), the noisy suppression term in Eq. (17), and the correlators I_2 and G_eta0 in Eqs. (19) and (22). The tau_Q^{-1/2} scaling is unaffected, but the alpha-dependent magnitudes and correlation lengths reported in the figures and discussion are quantitatively unreliable and must be recomputed.","section":null},{"comment":"The expansion of f_inf_alpha(k) around k=0 also has an incorrect linear term. The second term in Eq. (A1) should be zeta(alpha-1)/zeta(alpha) k, not zeta(1-alpha)/zeta(alpha) k. This is not a minor notational difference: zeta(alpha-1) diverges as alpha approaches 2, whereas zeta(1-alpha) does not, and the two coefficients have opposite signs in part of the range 1<alpha<2. Because F(k,alpha) in Eq. (14) and the prefactor R(alpha) in Eq. (15) are constructed from the square of this expansion, the noisy defect density and the anti-Kibble-Zurek magnitude inherit the error. The derivation should be redone with the correct second coefficient, and the comparison shown in Fig. 5 should be regenerated.","section":null},{"comment":"The manuscript does not state clearly whether the defect-density figures are computed from the exact Landau-Zener expressions p0_k and p_eta0_k or from the approximate formulas in Eqs. (11)-(17). This distinction matters because the approximate formulas contain the incorrect expansion coefficients. If the figures use exact numerics, the analytic equations should be corrected and compared with the exact curves; if the figures use the approximations, the plotted alpha-dependence may be an artifact. Please specify the numerical source and provide exact-versus-approximation comparisons of n(tau_Q) for at least two values of alpha in the long-range regime.","section":null},{"comment":"The noisy Landau-Zener result rests on the white-noise and fast-noise approximations: the phase is replaced by cos[bar(omega)(t)(t-t1)] and the integral limits are extended to infinity. The paper should state the quantitative conditions under which these replacements are valid for the parameter ranges used in Figs. 4-6, and should comment on how finite gamma or non-Markovian corrections could affect the two central noisy claims: the shift of dominant modes toward k=0 and the suppression of defects with decreasing alpha. Without such a discussion, the robustness of the anti-Kibble-Zurek conclusions to finite noise correlation time is not established.","section":null}],"minor_comments":[{"comment":"The abstract describes the drive as going from a paramagnetic phase with all spins down to one with all spins up; because the protocol crosses two quantum critical points and the final transverse field is large, the spin-state convention and the initial and final field values should be stated explicitly.","section":null},{"comment":"The approximation for I1(r) retains only the first two terms of a moment expansion; the text should state the condition under which this truncation is controlled, for example r^gamma/(chi tau_Q) much less than 1, and should note where the expansion begins to fail.","section":null},{"comment":"The longitudinal correlation function Cxx(r) is expressed as a Toeplitz determinant with g(r) defined by Eq. (28), but the sign convention is not fixed; the log-scale plots appear to show |Cxx|. Please state explicitly whether the plotted quantity is Cxx or its absolute value.","section":null},{"comment":"There are minor typographical issues: 'noise effects the coherence' should read 'affects', and in Eq. (B5) the noise correlation function should be written with explicit angle brackets after averaging over eta(t).","section":null}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this paper deserves a serious referee, but not because the numbers are ready to use. The combination of a two-critical-point long-range cluster Ising model, white noise, correlation functions, and kink statistics is genuinely new, and the qualitative pictures—α-independent n∝τ_Q^{−1/2}, anti-Kibble–Zurek behavior under noise, the shift of dominant modes to k=0, and Gaussian kink distributions—look robust. The paper is clearly written and the analytic LZ framework is applied honestly, with the fast-noise approximation stated openly. The shift of the noise-induced dominant mode from k=π to k=0 as α decreases is the most interesting result.\n\nThe soft spots are real. First, the stress-test is correct: near k=π the expansion of f∞α(k) has coefficient η(α−1)/ζ(α)=(1−2^{2−α})ζ(α−1)/ζ(α), not the ζ(1−α)/ζ(α) stated in Eq. (A2). Eq. (11) then uses ζ(α−1)/ζ(α), which is still not the right coefficient. This corrupts the prefactor B(α), the correlation length ξ0, and the noisy suppression term in Eq. (17). The τ_Q^{−1/2} scaling survives because the linear-in-δ form is correct, but the α-dependence of prefactors and correlation lengths is off. Second, the Landau–Zener exponent in Eq. (10) is inconsistent with Eq. (5). A standard LZ calculation with the Hamiltonian in Eq. (5) gives exp(−4πτ_Q f^2), not exp(−2πτ_Q f^2). This rescales all rates. Third, the abstract says the two-point fermionic correlator shows “quadratic suppression instead of power-law decay,” but the body explicitly gives an algebraic tail I1∝1/r^{2α−1} at large r. The abstract should be aligned. There is also a minor notation slip in Eq. (9), where p_k is written as the ground-state weight but later used as the excitation probability; the intended meaning is clear from the rest of the text.\n\nThese are mechanical errors, not deep conceptual ones. The qualitative claims and the overall structure should survive correction. The paper is for researchers working on quench dynamics in long-range or noisy systems, and it adds useful predictions for correlations and defect statistics beyond the standard short-range results. I would send it to peer review with the expectation that the authors fix the expansion coefficients and the LZ prefactor before publication. For my own work, I would not rely on the quoted numbers until those corrections appear.","headline":"Useful subfield contribution to KZ/AKZ physics in a long-range Ising model, but a wrong k=π expansion and a factor-of-two in the Landau–Zener exponent make the quantitative predictions unreliable as written.","tokens_in":20403,"tokens_out":19090,"would_cite":false,"duration_ms":199780,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Long-range Ising chain under adiabatic driving: noise reverses the effect of interaction range on defect density and shifts the controlling momentum mode from k=π to k=0.","keywords":["long-range Ising model","Kibble-Zurek mechanism","anti-Kibble-Zurek scaling","Landau-Zener transition","white noise","spin correlations","full counting statistics","transverse-field Ising chain"],"falsifier":"Compute the full noise-averaged Landau-Zener dynamics from Eq. (B5) at finite noise correlation time $\\gamma$ without the fast-noise replacement $\\cos[\\bar{\\omega}(t)(t-t_1)]$ and without extending the integral limits to infinity. If the noisy transition probability no longer peaks near $k=0$, or the defect density does not decrease as $\\alpha$ goes from $1.8$ to $1.25$ at fixed $\\eta_0^2\\tau_Q$, the central noisy claim is falsified.","tokens_in":19312,"feed_emoji":"⚛️","tokens_out":11077,"duration_ms":126491,"temperature":0.7,"pith_summary":"This paper asks how the range of a power-law interaction changes the defects and correlations produced when a transverse-field Ising chain is swept through its critical region, with and without noise. It establishes that in the noiseless long-range regime (interaction exponent $1<\\alpha<2$) the defect density scales as $n\\propto \\tau_Q^{-1/2}$, so the Kibble–Zurek exponent is independent of $\\alpha$, while the prefactor grows as $\\alpha$ decreases. In the presence of fast white noise, the trend reverses: longer-range couplings suppress defect formation, and the defect density follows the anti-Kibble–Zurek form $n\\simeq \\eta_0^2 \\tau_Q R(\\alpha)$ for small $\\eta_0^2\\tau_Q$. The same analysis yields the spatial profiles of fermionic and spin correlators and the full counting statistics of kinks from an exactly solvable fermionic mapping. A sympathetic reader would care because it gives a complete, parameter-free picture of which momentum modes control defect formation in long-range systems and how noise shifts that control from $k=\\pi$ to $k=0$.","feed_headline":"Noise flips how coupling range changes defect density in Ising chains","feed_subtitle":"Noiseless ramps keep Kibble-Zurek scaling; with noise, longer-range couplings suppress defects.","key_machinery":"The machinery is the Jordan-Wigner mapping of the long-range cluster Ising model with couplings $J_r = 1/(\\zeta(\\alpha)r^\\alpha)$ to a quadratic Kitaev-like fermionic chain whose momentum-space Hamiltonian breaks into independent two-level Landau-Zener problems. The load-bearing object is the antisymmetric pairing function $f_\\infty^\\alpha(k)=\\frac{1}{2i\\zeta(\\alpha)}[\\mathrm{Li}_\\alpha(e^{ik})-\\mathrm{Li}_\\alpha(e^{-ik})]$, whose asymmetric form for $1<\\alpha<2$ is responsible for the dominance of the $k=\\pi$ and later $k=0$ modes. The final state is the decohered density matrix $\\rho^s_k = p_k|0_k\\rangle\\langle 0_k| +(1-p_k)|k,-k\\rangle\\langle k,-k|$ built from the Landau-Zener probability $p_k$. For the noisy case, the argument uses the fast-noise approximation in which the noise-averaged equation's oscillatory phase is replaced by $\\cos[\\bar{\\omega}(t)(t-t_1)]$ and the time integral is extended to infinity, turning the noise into a delta-correlated damping term proportional to $\\eta_0^2 (f_\\infty^\\alpha)^2$; this produces the closed-form noisy transition probability $p^{\\eta_0}_k = \\frac{1}{2}[1+e^{-4\\pi\\tau_Q\\eta_0^2(f_\\infty^\\alpha)^2}(2p^0_k-1)]$.","core_discovery":"The central discovery is that the long-range interaction exponent $\\alpha$ does not change the universality class of defect production but does determine both the magnitude of defect density and the momentum modes responsible for it. Under a noiseless adiabatic ramp crossing two quantum critical points, defect density obeys $n\\propto \\tau_Q^{-1/2}$ for every $\\alpha>1$, with modes near $k=\\pi$ dominating; decreasing $\\alpha$ increases $n$. Under delta-correlated white noise, the dominant modes move to $k=0$, the defect density shows anti-Kibble–Zurek behavior (it grows with drive speed and noise strength) and is increasingly suppressed as $\\alpha$ decreases, which is the opposite of the noiseless trend. The paper also finds that two-point fermionic correlators in the long-range regime first decay as Gaussians and then are quadratically suppressed with separation, while longitudinal spin correlators decay exponentially; and the kink-number distribution remains approximately Gaussian, with higher cumulants proportional to the mean in the noiseless case and a characteristic crossover in the noisy case.","pith_inferences":["Editorial inference: because the noiseless enhancement is tied to the $k=\\pi$ critical point closing more gradually as $\\alpha$ decreases, a protocol that crosses only that single critical point should reproduce the enhancement; this would separate the two-critical-point geometry from the long-range effect itself.","Editorial inference: the fast-noise approximation becomes questionable exactly where $\\bar{\\omega}(t)\\to 0$ near the critical point; a finite-$\\gamma$ calculation should reveal a crossover from anti-Kibble-Zurek to Kibble-Zurek behavior as the noise slows, and the location of that crossover is testable.","Editorial inference: because the noise couples through $f_\\infty^\\alpha(k)$, which shrinks with decreasing $\\alpha$, the suppression of defects is a direct consequence of the interaction-range dependence of the pairing function; measuring the two-point correlator's Gaussian-to-quadratic crossover in an ion-trap or Rydberg simulator would provide a direct check."],"forward_implications":["For noiseless adiabatic ramps the Kibble–Zurek exponent stays $1/2$ for every $\\alpha>1$, while the defect-density prefactor grows as the interaction range increases.","Under white noise the defect density increases with $\\tau_Q$ and $\\eta_0^2$ (anti-Kibble–Zurek behavior), but longer-range interactions suppress that increase.","The optimal quench time retains the universal $\\tau_Q^{\\rm O}\\propto \\eta_0^{-4/3}$ scaling, with an $\\alpha$-dependent shift of where the minimum occurs.","In the long-range regime the two-point fermionic correlator shows Gaussian decay followed by quadratic suppression rather than a power law, for both noisy and noiseless protocols.","The kink-number distribution remains approximately Gaussian; in the slow-drive noisy regime the variance-to-mean ratio is independent of quench time."],"supporting_citations":[{"why":"Defines the long-range Ising model with cluster interactions and the $\\zeta(\\alpha)$ normalization that the paper drives across its two critical points.","marker":"[35]"},{"why":"Earlier long-range Kitaev-chain quench whose defect-density trend the paper directly contradicts in the noiseless two-critical-point protocol.","marker":"[27]"},{"why":"Companion long-range topological-superconductor scaling study providing the baseline for the exponent-independent noiseless result.","marker":"[28]"},{"why":"Previous study of a long-range pairing Kitaev chain with ramped quench and noise, providing the closest noisy long-range baseline.","marker":"[23]"},{"why":"Supplies the decohered density-matrix and Landau-Zener transition-probability formalism used for the final steady state and correlators.","marker":"[40]"},{"why":"Establishes anti-Kibble-Zurek behavior under noise in the short-range chain, the baseline the long-range noisy results are compared with.","marker":"[41]"},{"why":"Provides the full-counting-statistics cumulant machinery for the kink-number distribution used in Section V.","marker":"[29]"},{"why":"Shows universal defect statistics in the all-to-all LMG limit, the endpoint that the intermediate-$\\alpha$ statistics extend.","marker":"[33]"}],"fun_headline_variants":["Noise reverses how coupling range alters Ising defect density","Long-range Ising: noise flips the defect density trend","With noise, longer-range couplings suppress defects in Ising","Noise moves Ising defect modes from k=pi to k=0","In noisy Ising ramps, range suppresses defects instead of aiding"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the noise is effectively instantaneous (delta-correlated white noise), so the memory time of the noise can be ignored; if the noise has a finite correlation time, the predicted shift of the dominant modes to $k=0$ and the suppression of defect density with decreasing $\\alpha$ could change.","fun_headline_variants_meta":{"raw":{"variants":["Noise reverses how coupling range alters Ising defect density","Long-range Ising: noise flips the defect density trend","With noise, longer-range couplings suppress defects in Ising","Noise moves Ising defect modes from k=pi to k=0","In noisy Ising ramps, range suppresses defects instead of aiding"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000235,"raw_usage":{"total_tokens":1568,"prompt_tokens":1078,"completion_tokens":490,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":694,"completion_tokens_details":{"reasoning_tokens":402}},"tokens_in":694,"tokens_out":490,"duration_ms":5381,"temperature":1.0,"reasoning_tokens":402,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T00:48:17.269989+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full noise-averaged Landau-Zener dynamics from Eq. (B5) at finite noise correlation time $\\gamma$ without the fast-noise replacement $\\cos[\\bar{\\omega}(t)(t-t_1)]$ and without extending the integral limits to infinity. If the noisy transition probability no longer peaks near $k=0$, or the defect density does not decrease as $\\alpha$ goes from $1.8$ to $1.25$ at fixed $\\eta_0^2\\tau_Q$, the central noisy claim is falsified.","supporting_citations":[{"cited_title":"Fey and K","cited_arxiv_id":null,"evidence_quote":"Defines the long-range Ising model with cluster interactions and the $\\zeta(\\alpha)$ normalization that the paper drives across its two critical points."},{"cited_title":"Mattes, I","cited_arxiv_id":null,"evidence_quote":"Previous study of a long-range pairing Kitaev chain with ramped quench and noise, providing the closest noisy long-range baseline."},{"cited_title":"Sinha, D","cited_arxiv_id":null,"evidence_quote":"Supplies the decohered density-matrix and Landau-Zener transition-probability formalism used for the final steady state and correlators."}],"review_version":1}