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REVIEW 3 major objections 5 minor 52 references

Pairing correlation of the Kagome-lattice Hubbard model with the nearest-neighbor interaction

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read In the Kagome-Hubbard model, adding nearest-neighbor attraction switches the dominant pairing from next-nearest-neighbor d-wave to nearest-neighbor p-wave.

desk verdict 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. read the letter →

arxiv 2501.00251 v1 pith:QXIOBRND submitted 2024-12-31 cond-mat.str-el

Chen Yang , Chao Chen , Runyu Ma , Ying Liang , Tianxing Ma This is my paper · ORCID
classification cond-mat.str-el
keywords kagomelatticeHubbardmodelconstrainedpathMonteCarlopairingsymmetrysuperconductivityAV3Sb5next-nearest-neighbord-wavenearest-neighborp-wave
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

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.

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 (3)
  1. [Results & Discussions, Figs. 3, 5, 6, 7] 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.
  2. [Theoretical method] 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.
  3. [Results & Discussions, Figs. 5, 6, 8] 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.
minor comments (5)
  1. [Results & Discussions, Fig. 6(c)] 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).
  2. [Theoretical method, Eq. (3)] 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.
  3. [Abstract and Introduction] 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.
  4. [Theoretical method] 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.
  5. [Fig. 2 caption] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the dominant pairing symmetries are computed observables from fixed Hamiltonian inputs (U, V), not fitted parameters or outputs defined by construction.

full rationale

The paper's derivation chain is a direct constrained-path Monte Carlo (CPMC) calculation of pairing correlation functions C_alpha(r) for the Kagome-lattice Hubbard model with on-site U and nearest-neighbor V. The Hamiltonian (Eq. 1) treats U and V as independent inputs, and the pairing correlation functions (Eqs. 2-3) are measured ground-state observables; the dominant symmetry is read off from the relative magnitudes of C_alpha(r), not imposed by any fit. No parameter is tuned to reproduce the NNN-d or NN-p dominance, and the V=-1 conclusion is simply the computed response of the model to an attractive nearest-neighbor interaction. The five pairing form factors are taken from an external reference [36] as an ansatz, which is standard and not circular. The only self-citations (refs. 50-52) support the routine choice of a free-electron trial wavefunction and do not supply the central result. The unsupported assertion that 'the systematic error induced by the constraint is within a few percent' is a benchmark/robustness concern, not a circularity, because the constrained-path error is independent of the paper's conclusions. The V=0 NNN-d result is internally checked at L=9 (Fig. 8), and even the V=-1 result is a direct output of the simulation. Thus the paper is self-contained in the sense relevant to circularity: no equation reduces to its own input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The calculation rests on parameter choices (U=3.0, V=-1.0, special fillings) and method assumptions (CPMC bias, five-channel basis, single-band model). No new physical entities are introduced.

free parameters (3)
  • U = 3.0
    On-site Coulomb repulsion fixed to 3.0 (t=1). Results are demonstrated only at this value; no U dependence scan is shown.
  • V = -1.0 (also 0.0 and 1.0 in scans)
    Nearest-neighbor interaction chosen by hand; the central NN-p dominance claim is made at V=-1.0, a single attractive value.
  • electron fillings = ⟨n⟩ ≈ 0.630, 0.704, 0.981
    Closed-shell fillings chosen around the Dirac point (≈0.667) and near half-filling; the dominant-symmetry claim is tied to these special fillings.
assumptions (3)
  • domain assumption The constrained-path approximation in CPMC has a systematic error of only a few percent and does not change the ordering of pairing correlations.
    Invoked in 'Theoretical method' to justify using CPMC; no verification is provided for the V=-1 runs or for pairing correlations specifically.
  • domain assumption The five pairing form factors of Ref. [36] (NN-s, NN-d, NN-p, NNN-d, NNN-p) form a sufficient basis for identifying the dominant pairing symmetry.
    The paper compares only these five channels and does not consider, for example, f-wave or mixed-parity order parameters.
  • domain assumption The single-band Kagome-lattice Hubbard model captures the essential pairing physics of AV3Sb5.
    Used in the Introduction to motivate the model; the material has multiple orbitals, spin-orbit coupling, and charge-density-wave order not present in Eq. (1).

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Cite this review

Pith. "Pith review of Pairing correlation of the Kagome-lattice Hubbard model with the nearest-neighbor interaction." pith.science (2026). https://pith.science/paper/QXIOBRND

@misc{pith2026250100251,
  author       = {Pith},
  title        = {Pith review of: Pairing correlation of the Kagome-lattice Hubbard model with the nearest-neighbor interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QXIOBRND}},
  note         = {Machine review of arXiv:2501.00251}
}
abstract

A recently discovered family of Kagome lattice materials, $\emph{A}\mathrm{V}_{3}\mathrm{Sb}_{5}$($\emph{A}$= $\mathrm{K,Rb,Cs}$), has attracted great interest, especially in the debate over its dominant superconducting pairing symmetry. To explore this issue, we study the superconducting pairing behavior within the Kagome-Hubbard model through the constrained path Monte Carlo method. It is found that doping around the Dirac point generates a dominant next-nearest-neighbour-$d$ pairing symmetry driven by on-site Coulomb interaction $U$. However, when considering the nearest-neighbor interaction $V$, it may induce nearest-neighbor-$p$ pairing to become the preferred pairing symmetry. Our results provide useful information to identify the dominant superconducting pairing symmetry in $\emph{A}\mathrm{V}_{3}\mathrm{Sb}_{5}$ family.

Figures

Figures reproduced from arXiv: 2501.00251 by the authors.

Figure 1
Figure 1. FIG. 1: (a)The Structure of the Kagome lattice with lattice vectors [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Pairing symmetries between the sites in the Kagome [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Pairing correlations [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: FIG. 5: Pairing correlations [PITH_FULL_IMAGE:figures/full_fig_p003_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Pairing correlations [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Long-range part of NN- [PITH_FULL_IMAGE:figures/full_fig_p004_7.png]

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