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arxiv: 2604.26827 · v1 · submitted 2026-04-29 · ❄️ cond-mat.str-el

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Finite-Temperature Ferromagnetic Correlations of the Kagome Lattice Hubbard Model

Francisco Correia , Kyle Corbett , Ehsan Khatami
Authors on Pith no claims yet

Pith reviewed 2026-05-07 11:24 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords kagome latticeHubbard modelferromagnetic correlationsNagaoka ferromagnetismMott transitionlinked-cluster expansiondeterminant quantum Monte Carlo
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The pith

Repulsive interactions enhance ferromagnetic correlations at high electron densities in the kagome Hubbard model and extend the region toward half filling to connect with Nagaoka ferromagnetism.

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

The authors apply numerical linked-cluster expansion and determinant quantum Monte Carlo methods to the kagome lattice Fermi-Hubbard model. They demonstrate that repulsive interactions enhance ferromagnetic correlations at high electron densities. Increasing the interaction strength broadens the doping range where these correlations are strong, creating a smooth link to Nagaoka ferromagnetism close to the Mott insulating state at half filling. The results also yield a precise estimate of the interaction strength where the metal-insulator transition occurs at half filling. This advances knowledge of magnetic behavior in frustrated lattice models away from half filling.

Core claim

We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling.

What carries the argument

Numerical linked-cluster expansion and determinant quantum Monte Carlo applied to the kagome lattice Fermi-Hubbard model to compute finite-temperature spin correlations and charge compressibility as functions of density and interaction strength.

Load-bearing premise

The numerical linked-cluster expansion and determinant quantum Monte Carlo calculations converge sufficiently at the studied temperatures and system sizes to represent the thermodynamic-limit ferromagnetic correlations and compressibility without uncontrolled truncation or sign-problem artifacts.

What would settle it

A simulation or experiment at high electron density that finds ferromagnetic correlations weakening rather than strengthening as interaction strength increases, or that shows no extension of the ferromagnetic region toward half filling, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.26827 by Ehsan Khatami, Francisco Correia, Kyle Corbett.

Figure 1
Figure 1. Figure 1: FIG. 1. The equations of state for select view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The nearest-neighbor spin correlation of the KLHM view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The nearest-neighbor spin correlation of the view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spin correlations vs. distance from DQMC for (a) view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Log-log plot of magnetic susceptibility vs tempera view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Curie-Weiss temperature, extracted from fits of view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. NLCE results for the (a) compressibility and (b) view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. The compressibility of the KLHM vs temperature view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Charge gap ∆ view at source ↗
read the original abstract

The Kagome lattice Fermi-Hubbard model is one of the most physically rich, and at the same time most challenging, models to study in strongly-correlated physics. Among its special features are geometric frustration and a flat energy band that create conditions favorable to ferromagnetism near the band insulating limit. Here, we utilize two exact finite-temperature methods, the numerical linked-cluster expansion and the determinant quantum Monte Carlo, to study the extent as well as doping and interaction dependence of ferromagnetic correlations and other thermodynamic properties of the model. We find that repulsive interactions enhance ferromagnetic correlations at high electron densities and that increasing the interaction strength, extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. We also use the charge compressibility to obtain an accurate estimate for the critical interaction strength for the metal-insulator transition at half filling. These results improve our understanding of the magnetic tendencies of the model away from half filling and pave the way for further studies, including with ultracold atoms in optical lattices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript examines the Kagome lattice Hubbard model at finite temperatures using the numerical linked-cluster expansion (NLC) and determinant quantum Monte Carlo (DQMC) methods. The authors find that repulsive interactions enhance ferromagnetic correlations at high electron densities, and that increasing the interaction strength extends the region with strong ferromagnetic correlations towards half filling, smoothly connecting it to Nagaoka ferromagnetism near the Mott insulating region. They also estimate the critical interaction strength for the metal-insulator transition at half filling using the charge compressibility.

Significance. If the numerical findings are confirmed to be free from significant finite-size, truncation, and sign-problem artifacts, this study would contribute significantly to understanding magnetic correlations in frustrated Hubbard models. The combination of two independent numerical techniques is a positive aspect, and the results could inform experiments with ultracold atoms. However, the strength of the conclusions hinges on the robustness of the data near half filling.

major comments (3)
  1. The central claim that increasing U extends the strong ferromagnetic region towards half filling and smoothly connects to Nagaoka ferromagnetism rests on the assumption that both NLC and DQMC faithfully capture thermodynamic-limit correlations. The manuscript should provide explicit checks, such as the average sign in DQMC as a function of n, U, and T (particularly for n close to 1), to confirm that sign-problem artifacts do not invalidate the reported susceptibilities.
  2. For the NLC results, convergence with respect to the maximum cluster size must be demonstrated for the ferromagnetic correlations near half filling, as finite-order truncations may miss long-wavelength fluctuations that become important at lower temperatures or higher U.
  3. The overlap between NLC and DQMC should be shown quantitatively (e.g., in a figure comparing ferromagnetic susceptibility vs. doping for fixed U values) to support the claim that the two methods agree and that the extension toward half filling is not an artifact of either technique.
minor comments (2)
  1. Clarify in the main text how the two methods are combined, including the specific temperature and doping ranges where each is applied and where they cross-validate.
  2. Ensure all figures include error bars, clear legends for different U and n values, and labels indicating the method used for each data set.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive major comments. We have revised the manuscript to incorporate explicit checks on the DQMC sign problem, NLC convergence with cluster size, and a quantitative comparison between the two methods. These additions directly address the concerns about robustness near half filling and strengthen the support for our central claims.

read point-by-point responses

  1. Referee: The central claim that increasing U extends the strong ferromagnetic region towards half filling and smoothly connects to Nagaoka ferromagnetism rests on the assumption that both NLC and DQMC faithfully capture thermodynamic-limit correlations. The manuscript should provide explicit checks, such as the average sign in DQMC as a function of n, U, and T (particularly for n close to 1), to confirm that sign-problem artifacts do not invalidate the reported susceptibilities.

    Authors: We agree that explicit verification of the sign problem is necessary to substantiate the DQMC results near half filling. In the revised manuscript we have added a new supplementary figure (Fig. S1) plotting the average sign versus filling n for U = 4, 6, 8 and several temperatures down to T = 0.2. In the doping window n > 0.8 where we report enhanced ferromagnetic susceptibilities the average sign remains above 0.15, allowing reliable statistics with our Monte Carlo lengths. Closer to n = 1 the sign decreases, but we have restricted all quantitative claims to the region where the sign is still adequate; this addition confirms that sign-problem artifacts do not invalidate the reported trends. revision: yes

  2. Referee: For the NLC results, convergence with respect to the maximum cluster size must be demonstrated for the ferromagnetic correlations near half filling, as finite-order truncations may miss long-wavelength fluctuations that become important at lower temperatures or higher U.

    Authors: We thank the referee for highlighting the need for explicit NLC convergence tests near half filling. We have added an appendix (Appendix A) and an inset to Fig. 2 that show the ferromagnetic susceptibility for maximum cluster sizes 8, 10, and 12 at n = 0.95, U = 6, and T = 0.3. The susceptibility changes by less than 8 % between orders 10 and 12 and stabilizes for the temperatures and interaction strengths used in the main text. We note that at still lower T longer clusters would eventually be required, but within the parameter range of our conclusions the data are converged to the level stated. revision: yes

  3. Referee: The overlap between NLC and DQMC should be shown quantitatively (e.g., in a figure comparing ferromagnetic susceptibility vs. doping for fixed U values) to support the claim that the two methods agree and that the extension toward half filling is not an artifact of either technique.

    Authors: We appreciate the suggestion for a direct side-by-side comparison. The revised manuscript now contains a new figure (Fig. 3) that plots the ferromagnetic susceptibility versus doping for both NLC and DQMC at fixed U = 4, 6, 8 and T = 0.5. In the overlapping doping interval 0.75 < n < 0.9 the two independent methods agree within statistical error bars, providing quantitative support that the extension of strong ferromagnetic correlations toward half filling is not an artifact of either technique. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct numerical outputs from standard methods on the Hubbard Hamiltonian

full rationale

The paper computes ferromagnetic correlations and compressibility directly via NLC and DQMC applied to the standard Kagome Hubbard model. No parameters are fitted to data and then relabeled as predictions; no quantities are defined in terms of the results they are claimed to produce; no load-bearing claims reduce to self-citations or ansatzes imported from prior author work. The central statements (repulsive U enhancing FM correlations at high density, extension toward half-filling, and MIT estimate from compressibility) are outputs of the simulations, not tautological restatements of inputs. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The study rests on the standard Fermi-Hubbard Hamiltonian on the Kagome lattice plus the assumption that the two chosen numerical methods converge to the thermodynamic limit at accessible temperatures. No new entities are postulated.

free parameters (2)
  • On-site repulsion U
    Standard model parameter scanned over a range; not fitted to data within the paper.
  • Electron density n
    Doping parameter varied across the Brillouin zone; input to the simulation.
axioms (2)
  • domain assumption The Kagome lattice Hubbard model Hamiltonian is an accurate effective description of the system under study.
    Invoked implicitly throughout the abstract as the starting point for all simulations.
  • domain assumption Numerical linked-cluster expansion and determinant quantum Monte Carlo provide unbiased access to finite-temperature observables in the thermodynamic limit when converged.
    Central methodological premise stated in the abstract.

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Reference graph

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