{"id":"9e355705-100f-4d12-935b-3b390fd708de","arxiv_id":"2501.00251","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In the Kagome-lattice Hubbard model, on-site U favors next-nearest-neighbor d-wave pairing, and a nearest-neighbor interaction V=-1 switches the dominant channel to nearest-neighbor p-wave pairing.","lead":"A numerical study of the Kagome lattice Hubbard model finds that repulsive on-site interactions favor next-nearest-neighbor d-wave pairing, while adding an attractive nearest-neighbor interaction shifts the dominant pairing to nearest-neighbor p-wave. The results speak to the unresolved pairing symmetry debate in the AV3Sb5 kagome superconductors.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"V-induced NN-p over NNN-d crossover rests on unbenchmarked CPMC systematic error and single-size data at V=-1.","rationale":"The reader's conditional verdict identifies the constrained-path approximation and the absence of finite-size checks in the V=-1 case as the key weaknesses. I agree with that assessment, but my stress-test sharpens it in two ways. First, the trial wave function is the noninteracting U=0,V=0 state even when the Hamiltonian includes an attractive V=-1.0; the constrained-path bias is therefore not expected to be uniformly 'within a few percent' across the parameter range studied, and no trial-wave-function sensitivity test is provided. Second, the quantitative significance of the NN-p over NNN-d separation is impossible to assess because no error bars are reported; the D_alpha(r/a>3) aggregate in Fig. 6(c) averages over very few long-distance points on a small lattice, so the apparent crossover could be statistical noise. These considerations do not disprove the central claim, but they do mean the current preprint does not yet provide the evidence needed to establish a V-controlled pairing crossover. The reader's CONDITIONAL verdict is therefore appropriate, and my critique does not move the verdict. I credit the paper for using a standard method, for showing the L=9 check at V=0, and for being transparent about the constrained-path approximation at a methodological level; the missing pieces are the benchmarks, error bars, and a finite-size check specifically at V=-1.0.","tokens_in":9076,"tokens_out":4355,"duration_ms":47141,"concrete_test":"Run the same CPMC calculation at V=-1.0, U=3.0, and electron filling near n=0.704 on the L=9 lattice (or the largest available closed-shell cluster), computing D_alpha(r/a>3) for all five pairing channels with at least five independent Monte Carlo seeds to obtain standard errors. If NN-p no longer exceeds NNN-d on this larger lattice, the crossover is likely a finite-size effect. Independently, repeat the L=6 calculation at V=-1.0 with a different trial wave function, for instance one that includes a mean-field treatment of the V term or a BCS-type p-wave trial, and verify that the relative ordering of NN-p and NNN-d is unchanged within statistical error. If the ordering is stable under both changes, the concern is resolved; if not, the central claim is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that V=-1.0 switches the dominant pairing from NNN-d to NN-p, which would be a concrete prediction for AV3Sb5. For this claim to hold, the constrained-path Monte Carlo (CPMC) systematic error must be smaller than the gap between NN-p and NNN-d correlation functions at V=-1.0. The manuscript asserts that 'the systematic error induced by the constraint is within a few percent' but provides no benchmark calculations, no error bars, and no raw data for the pairing correlations. The trial wave function is the free-electron U=0, V=0 Slater determinant even for the V=-1.0 Hamiltonian, and no sensitivity test to this choice is reported. Because an attractive nearest-neighbor interaction can significantly alter the ground-state nodal structure, the constrained-path bias may be larger at V=-1.0 than at V=0, where the benchmark claim originates. In addition, the V=-1.0 result is shown only for one lattice size (3x6^2, L=6); the L=9 finite-size check in Fig. 8 is carried out at V=0 and only confirms NNN-d dominance, not the crossover. If the NN-p versus NNN-d separation in Fig. 5 or in D_alpha(r/a>3) in Fig. 6(c) is comparable to the unreported statistical and systematic uncertainties, then the headline conclusion is not yet established. This is not to say the result is false; rather, the evidence as presented does not rule out a constraint-induced bias or a finite-size artifact.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies the ground-state pairing correlations of the Kagome-lattice Hubbard model with an on-site Coulomb interaction U and a nearest-neighbor interaction V, using constrained-path Monte Carlo (CPMC) on 3×L² lattices with closed-shell fillings. The authors report that for U=3.0 and V=0, the next-nearest-neighbor d-wave (NNN-d) pairing correlation dominates near the Dirac point, and that adding V=-1.0 makes the nearest-neighbor p-wave (NN-p) pairing correlation the largest, suggesting a V-controlled pairing crossover relevant to the AV3Sb5 superconductors. The paper also presents a filling dependence of the leading correlations and a single larger-lattice check at V=0.","tokens_in":9292,"tokens_out":3432,"duration_ms":38778,"significance":"If the reported crossover is correct, it provides a concrete prediction for the Kagome-lattice Hubbard model: a negative nearest-neighbor interaction can switch the dominant pairing from NNN-d to NN-p, which would be directly relevant to the ongoing debate about pairing symmetry in AV3Sb5. The study uses a well-established quantum Monte Carlo approach with no fitted parameters, and it compares several pairing symmetries on an equal footing, which are genuine strengths. However, the numerical evidence as presented is incomplete: no statistical error bars are given for any correlation function, the constrained-path systematic error is asserted rather than demonstrated for this model and parameter regime, and the central V=-1 conclusion rests on a single interaction value at a single lattice size. These gaps currently limit the strength of the claim that can be drawn from the data.","major_comments":[{"comment":"No statistical uncertainties are reported for any Cα(r) or for the integrated quantities in Fig. 6(c). The central claim that NN-p surpasses NNN-d at V=-1.0 depends on the relative ordering of correlation curves; without error bars, convergence statistics, or raw numerical values, the reader cannot judge whether the ordering exceeds the Monte Carlo noise. Please provide error bars or a table of the long-range correlations with standard errors for all relevant parameter sets.","section":"Results & Discussions, Figs. 3, 5, 6, 7"},{"comment":"The statement that 'the systematic error induced by the constraint is within a few percent' is not supported by any benchmark shown for the present model or parameter regime. Because the trial wave function is the U=0, V=0 free-electron Slater determinant even when the Hamiltonian contains V=-1.0, the constrained-path bias at V=-1.0 could differ from the V=0 benchmarks. Please provide concrete evidence, for example exact-diagonalization comparisons on small clusters, trial-wavefunction sensitivity tests, or walker-population scaling, specifically for the pairing correlations at V=-1.0.","section":"Theoretical method"},{"comment":"The V-induced crossover conclusion is based on a single negative value V=-1.0 on the L=6 lattice. The finite-size check in Fig. 8 is performed only at V=0.0 (U=3.0, Nup=Ndn=83, L=9) and confirms NNN-d dominance, but it does not test whether NN-p remains dominant at V=-1.0 on a larger lattice. Please add a finite-size check for the V=-1.0 case and, ideally, at least one additional negative V value so that the crossover is not inferred from a single parameter point.","section":"Results & Discussions, Figs. 5, 6, 8"}],"minor_comments":[{"comment":"The quantity Dα(r/a > 3) is used to draw the conclusion that negative V enhances NN-p pairing, but its definition is incomplete: the text says the correlations with distance larger than 3a are summed, yet no explicit formula or normalization is given. Please specify whether Dα is a sum or an average and how it relates to Cα(r) in Eq. (2).","section":"Results & Discussions, Fig. 6(c)"},{"comment":"The notation for spin-triplet versus spin-singlet pairing is ambiguous: the ± sign is not explicitly assigned to the two channels, and the triplet case appears to be written for the Sz=0 component only. Please state the convention clearly.","section":"Theoretical method, Eq. (3)"},{"comment":"The abstract describes the numerical results as 'unbiased', but the constrained-path approximation introduces a systematic bias that the authors themselves estimate as a few percent. Please revise the wording to 'statistically unbiased within the constrained-path approximation' or similar.","section":"Abstract and Introduction"},{"comment":"The Monte Carlo parameters are given as 1200 walkers, Δτ=0.05, and 40 blocks of 320 steps, but no equilibration or autocorrelation analysis is reported. Please state how many steps were discarded and how statistical independence of the blocks was verified.","section":"Theoretical method"},{"comment":"The orange and purple arrows for positive and negative pairing may be difficult to distinguish in grayscale print; please add different line styles or symbols in addition to colors.","section":"Fig. 2 caption"}],"recommendation":"major_revision","confidential_remarks":"The manuscript addresses a timely and important problem, and the qualitative scenario is physically plausible, but the evidence for the headline crossover is not yet complete. The missing error bars, the untested constrained-path bias at V=-1.0, and the absence of a V=-1.0 finite-size check are all fixable within the manuscript's scope. I would encourage the editor to request these additions along with a reproducibility statement, since no raw data or code are currently provided. The paper is within scope for cond-mat.str-el but should not be accepted in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new piece is the V-dependence: with U=3.0 and V=0, NNN-d dominates, consistent with earlier RPA/fRG proposals, but at V=-1.0 the NN-p correlation overtakes it. That is a concrete, falsifiable prediction for the AV3Sb5 pairing debate, and the CPMC method is a respectable tool for it. The U-only results corroborate prior work, so the comparison across V is the contribution. The D_alpha(r/a>3) plot in Fig. 6(c) is a sensible way to summarize the crossover, and the L=9 check at V=0 is a good-faith finite-size attempt.\n\nThe soft spots are real but not fatal. First, no statistical error bars appear anywhere, so I cannot tell whether the NN-p versus NNN-d gap at V=-1 is larger than the noise. The blanket statement that constrained-path systematic error is within a few percent comes from previous benchmarks, but it is not demonstrated for this model at this V, where the trial wave function is still the U=0,V=0 Slater determinant. An attractive V=-1 may change the nodal structure enough to enlarge the bias. Second, the V=-1 crossover rests on a single interaction value and a single lattice size; the L=9 check is done only at V=0, so it does not test the crossover itself. These are the two things a revision would need to fix: error bars (or at least raw data) and a finite-size run at V=-1, plus some trial-wave-function sensitivity.\n\nI want to stress that the central claim is not implausible. A negative nearest-neighbor interaction naturally boosts nearest-neighbor p-wave pairing, so the direction of the effect is physically sensible. The problem is that the evidence as presented does not rule out a constraint-induced artifact or a finite-size accident. This is exactly the kind of paper that should go to peer review—the question matters, the method is established, and the weaknesses are addressable. The reader's conditional verdict is fair, and the stress-test note lands on the right weaknesses. For my own work, I would not cite the V=-1 crossover as established until the missing benchmarks appear.\n\nWho gets value: researchers tracking pairing-symmetry proposals in kagome systems. It is a useful pointer, not a settled answer. Send it to referees, but ask for the missing error bars and a crossover check at larger L.","headline":"A plausible but under-supported claim that attractive nearest-neighbor V flips the dominant pairing from NNN-d to NN-p in the kagome Hubbard model; the numerical evidence lacks error bars and finite-size checks at the crossover.","tokens_in":710,"tokens_out":1698,"would_cite":false,"duration_ms":32404,"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":"In the Kagome-Hubbard model, adding nearest-neighbor attraction switches the dominant pairing from next-nearest-neighbor d-wave to nearest-neighbor p-wave.","keywords":["kagome lattice","Hubbard model","constrained path Monte Carlo","pairing symmetry","superconductivity","AV3Sb5","next-nearest-neighbor d-wave","nearest-neighbor p-wave"],"falsifier":"Repeat the $V=-1.0$ simulation on a $3\\times9^2$ lattice (or larger) with more random walkers and a smaller time step, and compare the long-range NN-$p$ and NNN-$d$ correlations; if NN-$p$ no longer stays above NNN-$d$, the claimed crossover is a finite-size or constrained-path artifact.","tokens_in":8806,"feed_emoji":"🔬","tokens_out":6572,"duration_ms":59431,"temperature":0.7,"pith_summary":"This paper uses constrained path Monte Carlo (CPMC) simulations to ask which superconducting pairing symmetry the Kagome-lattice Hubbard model prefers at low doping. For on-site repulsion $U=3.0$ and no nearest-neighbor interaction, the next-nearest-neighbor $d$-wave pairing correlation is the largest among five tested symmetries at fillings around the Dirac point. Turning on a negative nearest-neighbor interaction $V=-1.0$ reverses the order: nearest-neighbor $p$-wave pairing becomes dominant. The authors present this as a $V$-controlled pairing crossover that could help identify which of the experimentally debated pairing symmetries is realized in the AV$_3$Sb$_5$ Kagome superconductors.","feed_headline":"Nearest-neighbor attraction flips Kagome pairing to p-wave","feed_subtitle":"CPMC simulations show d-wave dominates with on-site U alone, but V=-1 reverses the order.","key_machinery":"The central object is the real-space pairing correlation $C_\\alpha(r)$, computed for five lattice-symmetry-adapted pairing form factors: NN-$s$, NN-$d$, NN-$p$, NNN-$d$, and NNN-$p$. The Hamiltonian is $H = -t\\sum_{\\langle i,j\\rangle,\\sigma} c^\\dagger_{i\\sigma}c_{j\\sigma} + U\\sum_i n_{i\\uparrow}n_{i\\downarrow} + V\\sum_{\\langle i,j\\rangle,\\sigma} n_{i\\sigma}n_{j\\sigma}$. The argument is carried by CPMC, a sign-avoiding ground-state projection method, together with the comparison of long-range parts $C_\\alpha(r)$ and their distance-integrated values $D_\\alpha(r/a>3)$: whichever symmetry has the largest long-range correlation is declared dominant.","core_discovery":"In the ground state of the Kagome-lattice Hubbard model at $U=3.0$ and closed-shell fillings near the Dirac point, the longest-range pairing correlations are dominated by next-nearest-neighbor $d$-wave pairing (NNN-$d$). When a nearest-neighbor interaction $V=-1.0$ is added, the nearest-neighbor $p$-wave (NN-$p$) correlation overtakes NNN-$d$; systematically, negative $V$ enhances NN-$p$, while both signs of $V$ suppress NNN-$d$, so the dominant symmetry shifts from NNN-$d$ to NN-$p$. The claim is made for $3\\times6^2$ lattices and checked once on a $3\\times9^2$ lattice for the $V=0$ case, which preserves NNN-$d$ dominance.","pith_inferences":["A natural extension is to map the crossover boundary in the $(U,V)$ plane; the paper tests only $U=3.0$ and $V=-1,0,+1$, so the shape of the $d$-wave-to-$p$-wave transition region is unknown.","Verifying the $V=-1.0$ ordering on $L=9$ or larger lattices, and with more random walkers, would test whether the claimed crossover is robust beyond the single $L=6$ lattice.","If an effective nearest-neighbor attraction arises from phonons or orbital effects in real Kagome metals, the predicted NN-$p$ dominance offers a testable route to the observed nodal superconducting behavior."],"forward_implications":["If the crossover is robust, the superconducting pairing symmetry of Kagome-lattice models depends sensitively on the sign and strength of nearest-neighbor interactions, not just on the on-site Hubbard $U$.","Around Dirac-point fillings with only $U$, experiments should look for nodal or sign-changing pairing consistent with NNN-$d$ symmetry rather than simple $s$-wave.","A negative effective $V$ selects triplet NN-$p$ pairing, so materials with strong nearest-neighbor attraction are candidate spin-triplet superconductors.","Since both positive and negative $V$ suppress NNN-$d$ pairing, adding nearest-neighbor interactions will not stabilize the $d$-wave channel; it only erodes it."],"supporting_citations":[{"why":"Supplies the five Kagome-lattice pairing form factors $f_\\alpha(\\delta_l)$ that define the real-space pairing symmetries compared in the paper.","marker":"[36]"},{"why":"Introduces the constrained path Monte Carlo method for fermion ground states that the paper uses to avoid the sign problem.","marker":"[47]"},{"why":"Establishes the pairing-correlation measurement approach in quantum Monte Carlo that underlies the calculation of $C_\\alpha(r)$.","marker":"[46]"},{"why":"Prior determinant quantum Monte Carlo study of the Kagome-lattice Hubbard model, the baseline whose pairing-symmetry conclusions this paper extends.","marker":"[34]"},{"why":"References for the free-electron $U=0$ trial wave function used in the CPMC projection.","marker":"[50–52]"}],"fun_headline_variants":["Kagome Hubbard: V flips d-wave to p-wave pairing","Nearest-neighbor V reverses Kagome pairing symmetry","Kagome model: negative V switches pairing from d to p","CPMC: Kagome pairing flips to p-wave with V=-1","Interaction V turns Kagome d-wave pairing to p-wave"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the constrained-path approximation error, which the authors say is a few percent, is small enough that the relative ordering of the computed pairing correlations is preserved.","fun_headline_variants_meta":{"raw":{"variants":["Kagome Hubbard: V flips d-wave to p-wave pairing","Nearest-neighbor V reverses Kagome pairing symmetry","Kagome model: negative V switches pairing from d to p","CPMC: Kagome pairing flips to p-wave with V=-1","Interaction V turns Kagome d-wave pairing to p-wave"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000167,"raw_usage":{"total_tokens":1218,"prompt_tokens":869,"completion_tokens":349,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":485,"completion_tokens_details":{"reasoning_tokens":262}},"tokens_in":485,"tokens_out":349,"duration_ms":3610,"temperature":1.0,"reasoning_tokens":262,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:55:08.272502+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the $V=-1.0$ simulation on a $3\\times9^2$ lattice (or larger) with more random walkers and a smaller time step, and compare the long-range NN-$p$ and NNN-$d$ correlations; if NN-$p$ no longer stays above NNN-$d$, the claimed crossover is a finite-size or constrained-path artifact.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the five Kagome-lattice pairing form factors $f_\\alpha(\\delta_l)$ that define the real-space pairing symmetries compared in the paper."},{"cited_title":"Zhang, J","cited_arxiv_id":null,"evidence_quote":"Establishes the pairing-correlation measurement approach in quantum Monte Carlo that underlies the calculation of $C_\\alpha(r)$."}],"review_version":1}