Pith. sign in

REVIEW 3 major objections 6 minor 2 cited by

The paper argues that in La3Ni2O7 thin films, the interlayer antiferromagnetic superexchange between Ni d_{3z^2-r^2} orbitals is weakened by about 27% relative to bulk at 29.5 GPa, while in-plane magnetic couplings remain nearly unchanged.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

In La3Ni2O7 thin films, the interlayer d3z2-r2 antiferromagnetic coupling is about 27% weaker than in bulk, in-plane coupling is nearly unchanged, and hole/electron doping is particle-hole asymmetric.

T0 review reviewed 2026-08-03 challenge →

load-bearing objection Solid numerical study with a useful qualitative picture, but the headline 27% reduction is not actually demonstrated in the body. the 3 major comments →

arxiv 2511.04739 v2 pith:KLBLYYCF submitted 2025-11-06 cond-mat.supr-con cond-mat.str-el

Superexchanges and Charge Transfer in the La₃Ni₂O₇ Thin Films

Yuxun Zhong , W\'ei W\'u , Dao-Xin Yao This is my paper
classification cond-mat.supr-con cond-mat.str-el PACS 74.20.Mn71.10.Fd75.10.Jm
keywords La3Ni2O7bilayer nickelatethin film superconductivityHubbard modelsuperexchangecharge transfer gapdeterminant quantum Monte Carlocellular dynamical mean-field theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

La3Ni2O7 thin films superconduct at ambient pressure, unlike the bulk material which requires about 30 GPa. This paper asks whether the film's electronic structure is truly equivalent to the high-pressure bulk, and argues it is not: in the film, the interlayer antiferromagnetic superexchange between Ni-d_{3z^2-r^2} orbitals is about 27% weaker than in bulk, while the in-plane magnetic couplings between Ni-d_{x^2-y^2} orbitals stay almost unchanged. As a result, the two magnetic couplings become comparable in films, and the out-of-plane correlation no longer dominates as strongly. The same calculations show the film has a smaller charge-transfer gap, and that holes and electrons dope into different sets of orbitals in a strongly asymmetric way. If correct, these results shift the picture of pairing in bilayer nickelate films from an interlayer-dominated model to one where both in-plane and out-of-plane superexchanges matter.

Core claim

The paper's central claim is that the effective magnetic Hamiltonian of La3Ni2O7 thin films differs quantitatively from that of bulk La3Ni2O7 at 29.5 GPa. Using an 11-band d–p Hubbard model with DFT-derived parameters, the authors compute the leading antiferromagnetic superexchange couplings: the interlayer J_⊥ (between d_{3z^2-r^2} orbitals on the two NiO2 layers) and the intralayer J_∥ (between d_{x^2-y^2} orbitals in the same plane). They find that film growth with biaxial compression suppresses the interlayer correlation by roughly 27% relative to bulk, while the intralayer correlation is essentially unchanged, so that the ratio J_∥/J_⊥ rises from about 60% in bulk to about 81% in film.

What carries the argument

The central object is the 11-band d–p Hubbard model with Ni 3d_{x^2-y^2}, 3d_{3z^2-r^2}, and seven O 2p orbitals per unit cell, parameterized by DFT-derived tight-binding hoppings and on-site energies. The exchange couplings J_⊥ and J_∥ are extracted from second-order perturbation theory (Eq. 2) and from spin-spin correlations measured in determinant quantum Monte Carlo and cellular dynamical mean-field theory. The charge-transfer gap is probed via the chemical-potential dependence of hole concentration, and orbital-resolved carrier distributions are obtained by tracking hole/electron occupation changes per orbital.

Load-bearing premise

The claimed 27% weakening of the interlayer coupling rests on comparing two different sets of DFT-derived tight-binding parameters — one for the film and one for the bulk at pressure — and the paper does not display the bulk correlation values in its figures; if those parameter sets are not mutually consistent, the reduction could be an artifact of the parameter choice.

What would settle it

Take one consistent DFT framework, relax both the free-standing film and the bulk at 29.5 GPa, derive the 11-band parameters for both, and compute the interlayer d_{3z^2-r^2} spin correlation at the same temperature; if the film value is not at least ~20% lower than bulk, the central claim fails. Alternatively, extract J_⊥ from magnetic excitations measured on the same film and on bulk at pressure.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The reduced interlayer superexchange offers a plausible microscopic explanation for why Tc in films (above 40 K) is lower than the bulk's pressure-mediated Tc (~80 K).
  • Effective t–J models for films must include the intralayer d_{x^2-y^2} superexchange on equal footing with the interlayer d_{3z^2-r^2} term; the film cannot be treated as a scaled copy of the bulk Hamiltonian.
  • The charge-transfer gap narrowing in films implies enhanced compressibility and a more itinerant, cuprate-like in-plane charge response, consistent with the appearance of Zhang-Rice-singlet-like excitations.
  • The particle-hole asymmetry of orbital occupation predicts that hole-doped and electron-doped films should have different superconducting phase diagrams; in particular, Sr-hole doping populates d_{3z^2-r^2} more than the same amount of electron doping.
  • Hund's coupling strongly suppresses orbital polarization at half-filling but not at the pristine hole-rich configuration, indicating the film's spin-state balance is filling-dependent.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the 27% reduction is intrinsic to strain, then strain engineering offers a continuous dial for the J_∥/J_⊥ ratio; one could look for a dome in Tc versus substrate lattice mismatch.
  • The predicted 3:1 in-plane preference for electron doping suggests electron-doped films (e.g., Th substitution) should exhibit a sharper crossover to a different pairing regime than Sr-doped films at the same nominal level.
  • A direct spectroscopic measurement of the interlayer exchange in films, e.g., by two-magnon Raman or resonant inelastic X-ray scattering, could confirm the reduced J_⊥ without relying on the single-band parameter comparison.
  • The stronger relative weight of intralayer correlations in films raises the question of whether a d-wave in-plane component of the pairing gap coexists with the interlayer s-wave component—an issue the paper leaves open.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper studies an 11-band d-p Hubbard model for La3Ni2O7 thin films, with tight-binding parameters taken from a DFT calculation, using determinant quantum Monte Carlo (DQMC) and cellular dynamical mean-field theory (CDMFT). The central claim is that the interlayer antiferromagnetic coupling between Ni-d3z2-r2 orbitals is reduced by about 27% in films relative to bulk La3Ni2O7 at 29.5 GPa, while in-plane couplings are largely unchanged. The paper also reports a reduced charge-transfer gap in films and an orbital-resolved particle-hole asymmetry upon doping. The evidence is based on spin-spin correlation functions, perturbative estimates of J_perp and J_parallel, and filling-vs-chemical-potential curves.

Significance. If substantiated, the film-vs-bulk difference in magnetic couplings would be an important step toward understanding ambient-pressure superconductivity in bilayer nickelate films. The manuscript has clear strengths: the DQMC calculations are numerically exact for the model and are presented with error bars and average sign values; CDMFT provides a complementary low-temperature check; and Eq. (2) gives an explicit perturbative formula for J with stated inputs. However, the central quantitative comparison between film and bulk is not directly documented in the manuscript, and the current presentation does not allow the reader to verify the 27% reduction claim.

major comments (3)
  1. [§3, Figure 3, Table I] The central 27% reduction claim is not supported by the displayed data. The abstract states a 27% reduction, but the body only says the suppression is 'much more prominent' for the interlayer d3z2-r2 component; Figure 3's caption does not identify film versus bulk symbols or give numerical values, and Table I lists J_perp and J_parallel only for the film. Moreover, the comparison is made at mu=0 rather than at matched hole concentration: for the film, mu=0 corresponds to n_h≈1.234 (Fig. 2(b) caption), while the bulk n_h at mu=0 is not stated. Since the two parameter sets come from different DFT calculations, the claimed ~27% may be a doping artifact. Please present the bulk correlation values and the bulk J_perp, J_parallel computed with the same formula, and compare at matched n_h (e.g., both at half-filling n_h=1 and both at the same doped filling).
  2. [§2 Model and method] The film and bulk parameter sets are not shown together. The film uses parameters from Ref. [56] and the bulk uses Refs. [4,15]; these may involve different DFT functionals, pseudopotentials, structural relaxations, and strain treatments. Because all film-vs-bulk conclusions rest on this comparison, the manuscript should include a side-by-side table of hoppings and onsite energies (including the double-counting inputs) for both sets and a discussion of their comparability. Without this, the quantitative comparison is only as reliable as the parameter transfer.
  3. [§4, Figure 4(a)] The statement that the film has a smaller charge-transfer gap rests on a qualitative comparison: 'the reduced flatness of the µ−n_h curve around n_h=1 for the film (compared to the bulk at this temperature [15]) should point to a smaller charge transfer gap.' The bulk curve is not shown, and the text acknowledges the gap is not fully open at T=0.3. Please overlay the bulk µ−n_h curve at the same temperature and model, or otherwise quantify the gap (e.g., inverse compressibility), before making this claim.
minor comments (6)
  1. [Throughout] Typos: 'Halmiltonian' in §2, 'chager gap' in §4, 'Theses findings' in the abstract, and 'DMQC' in the Figure 1 caption.
  2. [Figure 3 caption] The caption does not identify which symbols correspond to film and which to bulk. Please specify the symbol convention and, ideally, give the numerical values of the correlations in the text.
  3. [Eq. (2)] The notation t_pd1 and t_pd2 is not connected to the hopping parameters t1, t2, t3, t6 shown in Figure 1(a). A brief mapping would improve readability.
  4. [Figure 2 caption] The caption writes 'J=0.15U', but the text uses J_H for Hund's coupling. Please use consistent notation.
  5. [Table I] The phrase 'calculations are performed up to sixth-order precision' is unclear; specify what is sixth-order (perturbation order, numerical precision, or expansion in t/U).
  6. [References] Several references are incomplete (e.g., [45], [76], [78] list only arXiv identifiers without journal details), and some entries have inconsistent formatting.

Circularity Check

0 steps flagged

No significant circularity; the central correlations and J values are direct outputs of the stated 11-band model with independently published DFT parameters, not fitted or defined into existence.

full rationale

The paper's derivation chain is self-contained and non-circular. The 11-band d-p Hubbard model in Eq. (1) is fixed by hopping and on-site parameters taken from published DFT calculations (Ref. [56] for films, Refs. [4,15] for bulk). The perturbative superexchange formula Eq. (2) is a standard second-order expansion in the hopping integrals of that same model, so the J values in Table I are consequences of the model, not inputs. The DQMC and CDMFT spin correlations in Figs. 2-3 are numerical evaluations of the same Hamiltonian and therefore also follow from the model. No parameter is fitted to the predicted correlations, no experimental datum is used to tune the couplings, and no quantity is defined in terms of the quantity it is claimed to explain. The film-vs-bulk comparison does rely on parameters from Refs. [56] and [4,15], which include works by some of the present authors, but those are external computational inputs rather than conclusions imported from this paper. The possible lack of matched filling or unshown bulk values is a legitimate evidence/comparability concern, not a circularity: even if the 27% reduction were an artifact of different chemical-potential definitions or DFT setups, that would be a correctness issue, not a case of the prediction being equivalent to its input by construction. There is no self-definitional step, no fitted quantity renamed as a prediction, no uniqueness theorem imported from the authors' prior work, and no renaming of a known result. Accordingly, the circularity score is low.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The paper introduces no new physical entities. It relies on a published 11-band model with parameters from DFT. The main inputs are the Hubbard U and Hund's coupling JH, taken from prior literature, and the DFT-dependent tight-binding parameters. The central results are numerical outputs of this fixed model, so the ledger is modest.

free parameters (2)
  • Hubbard U = 7 eV
    Taken from prior literature (Refs. [15,61]) and treated as a fixed input; not fitted to any data in this paper.
  • Hund's coupling JH = 0.15 U
    Set to 0.15U based on constrained RPA results (Ref. [14]); a model choice, not fitted here.
axioms (5)
  • domain assumption The 11-band d-p Hubbard model (Eq. 1) captures the relevant low-energy physics of La3Ni2O7 thin films.
    The paper assumes that the chosen Ni-3d and O-2p orbitals are sufficient; higher-order terms and other orbitals are neglected. This is standard for nickelate models but not proven.
  • domain assumption The tight-binding parameters from Ref. [56] accurately describe the thin-film structure, and the bulk parameters from Refs. [4,15] describe bulk at 29.5 GPa.
    The entire film-vs-bulk comparison hinges on the validity and comparability of these DFT-derived parameter sets.
  • ad hoc to paper Held's double-counting correction (Eq. 1 text) is appropriate for this system.
    The double-counting formula is adopted from Ref. [73] with a computed n0_d ~ 2.14; this is a modeling choice that affects the effective orbital energies and thus the charge-transfer gap.
  • ad hoc to paper The neglect of pair-hopping and spin-flip terms in Hund's coupling is justified.
    The paper states these terms are neglected (after Eq. 1). This simplification could affect magnetic correlations and is not benchmarked.
  • domain assumption DQMC and CDMFT results at finite temperature (T=0.25 and T=0.08-0.125) are representative of the zero-temperature physics relevant for superconductivity.
    The accessible temperatures are high due to the sign problem; the authors infer ground-state properties from these temperatures without an explicit extrapolation.

reviewed 2026-08-03 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Superexchanges and Charge Transfer in the La$_3$Ni$_2$O$_7$ Thin Films." pith.science (2026). https://pith.science/paper/KLBLYYCF

@misc{pith2026251104739,
  author       = {Pith},
  title        = {Pith review of: Superexchanges and Charge Transfer in the La$_3$Ni$_2$O$_7$ Thin Films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KLBLYYCF}},
  note         = {Machine review of arXiv:2511.04739}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The recent discovery of ambient-pressure superconductivity with $T_c$ above 40 K in La$_3$Ni$_2$O$_7$ thin films represents a significant advance in the field of nickelate superconductor. Motivated by the experimental reports, here we study an 11-band $d-p$ Hubbard model with tight-binding parameters derived from \textit{ab initio} calculations, using large scale determinant quantum Monte Carlo and cellular dynamical mean-field theory. Our results reveal that the major superexchange couplings in La$_3$Ni$_2$O$_7$ thin films can be substantially weaker than in the bulk material at 29.5 Gpa. Specifically, the out-of-plane antiferromagnetic correlation between Ni$-d_{3z^2-r^2}$ orbitals is reduced by about 27\% in film, while the in-plane magnetic correlations remain largely unaffected. We evaluate the corresponding antiferromagnetic coupling constants, $J_{\perp}$ and $J_{\parallel}$ using perturbation theory. With regard to charge transfer properties, we find that the biaxial compression in films reduces charge transfer gap. We also resolve the orbital distribution of doped holes and electrons among the in-plane (Ni$-d_{x^2-y^2}$ and O$-p_x/p_y$) and the out-of-plane (Ni$-d_{3z^2-r^2}$ and O$-p_z$) orbitals, uncovering a pronounced particle-hole asymmetry. Theses findings lay a groundwork for the study of low-energy $t-J$ model of La$_3$Ni$_2$O$_7$ films and provide key insights into the understanding of physical distinctions between the film and bulk bilayer nickelates.

Figures

Figures reproduced from arXiv: 2511.04739 by Dao-Xin Yao, W\'ei W\'u, Yuxun Zhong.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the 11-band bilayer LNO thin film lattice [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The spin-spin correlation function [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Charge transfer properties and charge carrier evolution of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Nature of magnetism in bilayer nickelate La3Ni2O7 single crystals

    cond-mat.str-el 2026-05 unverdicted novelty 6.0

    Single-crystal neutron scattering establishes stripe antiferromagnetic order with strong interlayer coupling and competing in-plane exchanges in La3Ni2O7, yielding fluctuating moments comparable to cuprates but with l...

  2. Superconductivity in Ruddlesden-Popper nickelates: a review of recent progress, focusing on thin films

    cond-mat.supr-con 2026-04 unverdicted novelty 2.0

    The review covers experimental and theoretical progress on superconductivity in Ruddlesden-Popper nickelates, emphasizing ambient-pressure thin-film results in La3Ni2O7.

Reference graph

Works this paper leans on

78 extracted references · 10 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Sun H, Huo M, Hu X, Li J, Liu Z, Han Y , Tang L, Mao Z, Yang P, Wang B, Cheng J, Yao D X, Zhang G M, and Wang M 2023 Nature6217979

    2023

  2. [2]

    Zhu Y , Peng D, Zhang E, Pan B, Chen X, Chen L, Ren H, Liu F, Hao Y , Li N, Xing Z, Lan F, Han J, Wang J, Jia D, Wo H, Gu Y , Gu Y , Ji L, Wang W, Gou H, Shen Y , Ying T, Chen X, Yang W, Cao H, Zheng C, Zeng Q, Guo J g, and Zhao J 2024Nature 6318021

  3. [3]

    Li Q, Zhang Y J, Xiang Z N, Zhang Y , Zhu X, and Wen H H 2024Chin. Phys. Lett.411

  4. [4]

    Luo Z, Hu X, Wang M, W ´u W, and Yao D X 2023Phys. Rev. Lett.13112

  5. [5]

    Zhang Y , Lin L F, Moreo A, and Dagotto E 2023Phys. Rev. B 10818

  6. [6]

    Lechermann F, Gondolf J, B¨otzel S, and Eremin I M 2023Phys. Rev. B10820

  7. [7]

    Shilenko D A and Leonov I V 2023Phys. Rev. B10812

  8. [8]

    Chen X, Jiang P, Li J, Zhong Z, and Lu Y 2025Phys. Rev. B 1111

  9. [9]

    Ouyang Z, Gao M, and Lu Z Y 2024npj Quantum Mater .91

  10. [10]

    Liu Y B, Mei J W, Ye F, Chen W Q, and Yang F 2023Phys. Rev. Lett.13123

  11. [11]

    Heier G, Park K, and Savrasov S Y 2024Phys. Rev. B10910

  12. [12]

    Commun.151

    Zhang Y , Lin L F, Moreo A, Maier T A, and Dagotto E 2024 Nat. Commun.151

    2024

  13. [13]

    Zhang Y , Lin L F, Moreo A, Maier T A, and Dagotto E 2024 Phys. Rev. B1094

    2024

  14. [14]

    Christiansson V , Petocchi F, and Werner P 2023Phys. Rev. Lett. 13120

  15. [15]

    China Phys

    W ´u W, Luo Z, Yao D X, and Wang M 2024Sci. China Phys. Mech. Astron.6711

  16. [16]

    Tian Y H, Chen Y , Wang J M, He R Q, and Lu Z Y 2024Phys. Rev. B10916

  17. [17]

    Ryee S, Witt N, and Wehling T O 2024Phys. Rev. Lett.1339

  18. [18]

    Shen Y , Qin M, and Zhang G M 2023Chin. Phys. Lett.4012

  19. [19]

    Lu C, Pan Z, Yang F, and Wu C 2024Phys. Rev. Lett.13214

  20. [20]

    Oh H and Zhang Y H 2023Phys. Rev. B10817

  21. [21]

    Qu X Z, Qu D W, Chen J, Wu C, Yang F, Li W, and Su G 2024 Phys. Rev. Lett.1323

    2024

  22. [22]

    Yang H, Oh H, and Zhang Y H 2024Phys. Rev. B11010

  23. [23]

    Liao Z, Chen L, Duan G, Wang Y , Liu C, Yu R, and Si Q 2023 Phys. Rev. B10821

    2023

  24. [24]

    Fan Z, Zhang J F, Zhan B, Lv D, Jiang X Y , Normand B, and Xiang T 2024Phys. Rev. B1102

  25. [25]

    Kaneko T, Sakakibara H, Ochi M, and Kuroki K 2024Phys. Rev. B1094

  26. [26]

    Luo Z, Lv B, Wang M, W´u W, and Yao D X 2024npj Quantum Mater .91

  27. [27]

    Yang Q G, Wang D, and Wang Q H 2023Phys. Rev. B10814

  28. [28]

    Sakakibara H, Kitamine N, Ochi M, and Kuroki K 2024Phys. Rev. Lett.13210

  29. [29]

    Cao Y and Yang Y f 2024Phys. Rev. B1098

  30. [30]

    Yang Y f, Zhang G M, and Zhang F C 2023Phys. Rev. B108 20

  31. [31]

    Huang J, Wang Z, and Zhou T 2023Phys. Rev. B10817

  32. [32]

    Huang J, Wang Z D, and Zhou T 2023Phys. Rev. B10817

  33. [33]

    Jiang R, Hou J, Fan Z, Lang Z J, and Ku W 2024Phys. Rev. Lett.13212

  34. [34]

    Zhang J X, Zhang H K, You Y Z, and Weng Z Y 2024Phys. Rev. Lett.13312

  35. [35]

    Wang M, Wen H H, Wu T, Yao D X, and Xiang T 2024Chin. Phys. Lett.417

  36. [36]

    Commun.151

    Yang J, Sun H, Hu X, Xie Y , Miao T, Luo H, Chen H, Liang B, Zhu W, Qu G, Chen C Q, Huo M, Huang Y , Zhang S, Zhang F, Yang F, Wang Z, Peng Q, Mao H, Liu G, Xu Z, Qian T, Yao D X, Wang M, Zhao L, and Zhou X J 2024Nat. Commun.151

  37. [37]

    2024Nature Physics208

    Zhang Y , Su D, Huang Y , Shan Z, Sun H, Huo M, Ye K, Zhang J, Yang Z, Xu Y , et al. 2024Nature Physics208

  38. [38]

    2023Chinese Physics Letters4011

    Hou J, Yang P T, Liu Z Y , Li J Y , Shan P F, Ma L, Wang G, Wang N N, Guo H Z, Sun J P, et al. 2023Chinese Physics Letters4011

  39. [39]

    Fan S, Luo Z, Huo M, Wang Z, Li H, Yang H, Wang M, Yao D X, and Wen H H 2024Phys. Rev. B110

  40. [40]

    Wang G, Wang N N, Shen X L, Hou J, Ma L, Shi L F, Ren Z A, Gu Y D, Ma H M, Yang P T, Liu Z Y , Guo H Z, Sun J P, Zhang G M, Calder S, Yan J Q, Wang B S, Uwatoko Y , and Cheng J G 2024Phys. Rev. X14

  41. [41]

    2024Nature Communications151

    Liu Z, Huo M, Li J, Li Q, Liu Y , Dai Y , Zhou X, Hao J, Lu Y , Wang M, et al. 2024Nature Communications151

  42. [42]

    Li J, Peng D, Ma P, Zhang H, Xing Z, Huang X, Huang C, Huo M, Hu D, Dong Z, Chen X, Xie T, Dong H, Sun H, Zeng Q, Mao H k, and Wang M 2025National Science Review1210

  43. [43]

    Pan Z, Lu C, Yang F, and Wu C 2024Chinese Physics Letters 418

  44. [44]

    Zhang Y , Lin L F, Moreo A, Maier T A, and Dagotto E 2023 Phys. Rev. B108

    2023

  45. [45]

    Li F, Xing Z, Peng D, Dou J, Guo N, Ma L, Zhang Y , Wang L, Luo J, Yang J, Zhang J, Chang T, Chen Y S, Cai W, Cheng J, Wang Y , Zeng Z, Zheng Q, Zhou R, Zeng Q, Tao X, and Zhang J 2025arXiv2501.14584 6

    Pith/arXiv arXiv

  46. [46]

    Zhu F H, Wang X Y , Shao T N, Zhao Q, Yang W L, Chen C X, Yan M L, Dou R F, Xiong C M, and Nie J C 2025Chin. Phys. Lett.426

  47. [47]

    Osada M, Terakura C, Kikkawa A, Nakajima M, Chen H Y , Nomura Y , Tokura Y , and Tsukazaki A 2025Communications Physics81

  48. [48]

    Wang B Y , Zhong Y , Abadi S, Liu Y , Yu Y , Zhang X, Wu Y M, Wang R, Li J, Tarn Y , Ko E K, Thampy V , Hashimoto M, Lu D, Lee Y S, Devereaux T P, Jia C, Hwang H Y , and Shen Z X 2025 arXiv2504.16372

    Pith/arXiv arXiv 2025

  49. [49]

    Bhatt L, Jiang A Y , Ko E K, Schnitzer N, Pan G A, Segedin D F, Liu Y , Yu Y , Zhao Y F, Morales E A, Brooks C M, Botana A S, Hwang H Y , Mundy J A, Muller D A, and Goodge B H 2025 arXiv2501.08204

    Pith/arXiv arXiv 2025

  50. [50]

    Liu Y , Ko E K, Tarn Y , Bhatt L, Li J, Thampy V , Goodge B H, Muller D A, Raghu S, Yu Y , and Hwang H Y 2025Nature Materials

  51. [51]

    2025Nature6388052

    Ko E K, Yu Y , Liu Y , Bhatt L, Li J, Thampy V , Kuo C T, Wang B Y , Lee Y , Lee K, et al. 2025Nature6388052

  52. [52]

    2025Nature6408059

    Zhou G, Lv W, Wang H, Nie Z, Chen Y , Li Y , Huang H, Chen W Q, Sun Y J, Xue Q K, et al. 2025Nature6408059

  53. [53]

    Shao Z Y , Liu Y B, Liu M, and Yang F 2025arXiv2501.10409

    Pith/arXiv arXiv

  54. [54]

    Cao Y H, Jiang K Y , Lu H Y , Wang D, and Wang Q H 2025 arXiv2507.13694

    Pith/arXiv arXiv 2025

  55. [55]

    Samanta B and Georgescu A B 2025arXiv2506.11427

    Pith/arXiv arXiv

  56. [56]

    Hu X, Qiu W, Chen C Q, Luo Z, and Yao D X 2025 arXiv2503.17223

    arXiv 2025

  57. [57]

    Blankenbecler R, Scalapino D J, and Sugar R L 1981Phys. Rev. D24

  58. [58]

    Assaad F and Evertz H 2008 277–356Computational Many- Particle Physics277–356

    2008

  59. [59]

    Georges A, Kotliar G, Krauth W, and Rozenberg M J 1996Rev. Mod. Phys.68

  60. [60]

    Maier T, Jarrell M, Pruschke T, and Hettler M H 2005Rev. Mod. Phys.77

  61. [61]

    Karp J, Botana A S, Norman M R, Park H, Zingl M, and Millis A 2020Phys. Rev. X10

  62. [62]

    Zaanen J, Sawatzky G A, and Allen J W 1985Phys. Rev. Lett. 55

  63. [63]

    Ruan W, Hu C, Zhao J, Cai P, Peng Y , Ye C, Yu R, Li X, Hao Z, Jin C, Zhou X, Weng Z Y , and Wang Y 2016Science Bulletin 6123

  64. [64]

    Kowalski N, Dash S S, S ´emon P, S ´en´echal D, and Tremblay A M 2021Proceedings of the National Academy of Sciences 11840

  65. [65]

    Weber C, Yee C, Haule K, and Kotliar G 2012Europhysics Letters1003

  66. [66]

    O’Mahony S M, Ren W, Chen W, Chong Y X, Liu X, Eisaki H, Uchida S, Hamidian M H, and Davis J C S 2022Proceedings of the National Academy of Sciences11937

  67. [67]

    Rybicki D, Jurkutat M, Reichardt S, Kapusta C, and Haase J 2016Nature Communications71

  68. [68]

    Hao B, Wang M, Sun W, Yang Y , Mao Z, Yan S, Sun H, Zhang H, Han L, Gu Z, Zhou J, Ji D, and Nie Y 2025arXiv2505.12603

    Pith/arXiv arXiv

  69. [69]

    Mo S, Zheng Y , and Wu W 2025arXiv2508.04554

    arXiv

  70. [70]

    Bejas M, Wu X, Chakraborty D, Schnyder A P, and Greco A 2025Phys. Rev. B111

  71. [71]

    Zheng Y Y and W ´u W 2025Phys. Rev. B111

  72. [72]

    Held K, Keller G, Eyert V , V ollhardt D, and Anisimov V I 2001 Phys. Rev. Lett.86

    2001

  73. [73]

    Held K 2007Advances in physics566

  74. [74]

    Zhong H, Hao B, Wei Y , Zhang Z, Liu R, Huang X, Ni X S, dos Reis Cantarino M, Cao K, Nie Y , Schmitt T, and Lu X 2025 arXiv2502.03178

    Pith/arXiv arXiv 2025

  75. [75]

    Ren X, Sutarto R, Wu X, Zhang J, Huang H, Xiang T, Hu J, Comin R, Zhou X, and Zhu Z 2025Communications Physics8

  76. [76]

    Yue C, Miao J J, Huang H, Hua Y , Li P, Li Y , Zhou G, Lv W, Yang Q, Yang F, Sun H, Sun Y J, Lin J, Xue Q K, Chen Z, and Chen W Q 2025National Science Review

  77. [77]

    Qiu W, Luo Z, Hu X, and Yao D X 2025arXiv2506.20727

    Pith/arXiv arXiv

  78. [78]

    Shi H, Huo Z, Li G, Ma H, Cui T, Yao D X, and Duan D 2025 arXiv2502.04255

    Pith/arXiv arXiv 2025

This paper was first reviewed by deepseek-v4-flash on August 3, 2026.