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REVIEW 5 major objections 4 minor 35 references

Variational study of the magnetization plateaus of the spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet and its implication on YCOB

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The one-ninth magnetization plateau of the spin-1/2 kagome antiferromagnet is a windmill valence bond crystal, not a chiral spin liquid.

desk verdict A genuinely more general RVB ansatz finds a new windmill VBC at the 1/9 plateau, but missing error bars and an uncontrolled comparison to the prior chiral spin liquid keep the conclusion from being airtight. read the letter →

arxiv 2507.20308 v1 pith:57C55OZC submitted 2025-07-27 cond-mat.str-el

Rong Cheng , Tao Li This is my paper · ORCID
classification cond-mat.str-el
keywords kagomeantiferromagnetmagnetizationplateauvalencebondcrystalresonatingvariationalMonteCarlofinite-depthBFGSYCOBfrustratedquantummagnetism
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 argues that the controversial one-ninth magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet is a valence bond crystal with a windmill-shaped 27-site motif repeated with $3\times3$ periodicity, not a $Z_3$ chiral spin liquid. The authors reach this by optimizing the most general fermionic resonating-valence-bond wavefunction consistent with the model's $U(1)$ spin symmetry, using a finite-depth BFGS algorithm that handles large parameter sets on a 432-site cluster. At the plateau the optimized energy is $E(M)\approx -0.4184\,J/\mathrm{site}$, below the previously claimed chiral spin liquid energy of about $-0.4116\,J/\mathrm{site}$ and the earlier $\sqrt{3}\times\sqrt{3}$ valence bond crystal energy of about $-0.4111\,J/\mathrm{site}$. The same ansatz reproduces the known David-star $\sqrt{3}\times\sqrt{3}$ valence bond crystals at the one-third, five-ninths, and seven-ninths plateaus, and predicts that local magnetization is always strongly nonuniform below the saturation field. If correct, this assigns the experimentally observed one-ninth plateau in the kagome spin-liquid candidate YCOB to a symmetry-broken valence bond crystal rather than a spin liquid.

What carries the argument

The carrying object is a fully general fermionic resonating-valence-bond (RVB) wavefunction: a Gutzwiller-projected Slater determinant built from a mean-field BCS-type Hamiltonian whose hopping and pairing amplitudes are arbitrary complex numbers between all pairs of sites, with only spin-rotation symmetry about the field direction imposed. The variational parameters are taken to be the matrix elements of the first $2N_e^{\uparrow}$ columns of the diagonalizing unitary matrix, which makes the wavefunction free to break any spatial symmetry and makes energy gradients cheap to compute. The companion optimizer is the finite-depth BFGS quasi-Newton method, which reconstructs an approximate inverse Hessian from a short history of parameter and gradient updates, so a system with roughly 660,000 parameters can be optimized without storing a dense $10^{12}$-entry Hessian. This pair of tools converts the contest between the chiral spin liquid, the $\sqrt{3}\times\sqrt{3}$ valence bond crystal, and the windmill crystal into a single unbiased optimization problem.

What would settle it

An independent, high-precision DMRG or tensor-network calculation on a 432-site (or larger) kagome cluster at magnetization one-ninth that reaches an energy below $-0.4184\,J/\mathrm{site}$ without the $3\times3$ windmill pattern, or that reproduces the $Z_3$ chiral spin liquid energy and pattern, would disprove the paper's central claim. A complementary experimental check is nuclear magnetic resonance on YCOB at the one-ninth plateau: resolving a $3\times3$ periodic local magnetization pattern with reversed polarization would support the claim, while spatially uniform local magnetization would contradict it.

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Extended reading notes

Core claim

The central discovery is that the ground state at the one-ninth magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet is a translational-symmetry-broken valence bond crystal with $3\times3$ periodicity and a windmill-shaped unit cell of 27 sites. After unrestricted variational optimization with no spatial symmetry assumed, the energy at this plateau on a 432-site cluster is $E(M)\approx -0.4184\,J/\mathrm{site}$, clearly below the $Z_3$ chiral spin liquid state of a previous variational study and below the $\sqrt{3}\times\sqrt{3}$ valence bond crystal found by tensor network simulations. The windmill pattern shows sixfold rotational symmetry in its local spin correlations; the magnetization is concentrated on nine sites of three dumbbells, and on the center site of each dumbbell the local magnetization is polarized opposite to the external field. The same general ansatz reproduces the David-star valence bond crystals at the one-third, five-ninths and seven-ninths plateaus, and generates a magnetization curve with all four plateaus in field ranges close to earlier numerical estimates.

Load-bearing premise

The calculation assumes the true ground state can be represented by a single optimized quantum wavefunction of the resonating-valence-bond type; if the real one-ninth plateau state needs a superposition of several such wavefunctions, or a different kind of state entirely, the energy comparison that favors the windmill crystal is biased.

Editorial extensions

If this is right

  • The one-ninth magnetization plateau is a symmetry-breaking valence bond crystal, so explaining it does not require a topological $Z_3$ chiral spin liquid.
  • All four magnetization plateaus of the spin-1/2 kagome Heisenberg antiferromagnet are valence bond crystals: the one-third, five-ninths, and seven-ninths plateaus share the David-star $\sqrt{3}\times\sqrt{3}$ pattern, while the one-ninth plateau uses the windmill pattern.
  • Below the saturation field the local magnetization is never uniform, and its relative inhomogeneity diverges as the inverse square root of the average magnetization toward zero field, so homogeneous-magnetization approximations fail for this magnet even in weak fields.
  • For YCOB, the measured one-ninth plateau and the unconventional torque oscillations should be attributed to the windmill valence bond crystal and the accompanying spatial magnetization modulation, not to a chiral spin liquid.
  • The finite-depth BFGS optimizer makes unrestricted variational optimization with millions of parameters practical, so the same unbiased search can be applied directly to other strongly frustrated spin models.

Reading between the lines

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

  • An implication the authors leave implicit is that the windmill valence bond crystal should produce a distinctive real-space fingerprint in local probes such as nuclear magnetic resonance on YCOB: a $3\times3$ periodic pattern in the Knight shift with sign-reversed polarization at the dumbbell centers.
  • Because the energy landscape among translational symmetry-breaking patterns at the one-ninth plateau is nearly flat, an independent check of the claim would be to map how the preferred pattern depends on cluster shape and boundary conditions in DMRG or tensor network calculations; the windmill pattern should be systematically favored on large, periodic clusters.
  • The predicted $1/\sqrt{m}$ divergence of relative inhomogeneity implies that even an infinitesimal field creates strongly nonuniform local moments; if confirmed in YCOB at very low fields, this intrinsic inhomogeneity would need to be separated from the material's known disorder before interpreting any local measurements.
  • A testable extension of the method is to apply the same unrestricted RVB optimization to the triangular-lattice Heisenberg antiferromagnet at its one-third plateau, where the same question of chiral spin liquid versus valence bond crystal has also been debated.
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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

5 major / 4 minor

Summary. The paper studies the magnetization plateaus of the spin-1/2 kagome Heisenberg antiferromagnet using a variational Monte Carlo approach based on a general long-range fermionic resonating-valence-bond (RVB) ansatz optimized with a finite-depth BFGS algorithm. For fixed total magnetization, the authors compute variational energies on N=108 and N=432 site clusters, extract the magnetization curve by a Maxwell construction, and identify the 1/9 plateau as a 3x3 valence bond crystal with a windmill-shaped 27-site motif at E ≈ -0.4184 J/site. This energy is compared with E ≈ -0.4116 J/site for the previously proposed Z3 chiral spin liquid and E ≈ -0.4111 J/site for a tensor-network sqrt(3)xsqrt(3) VBC. The paper further claims that the 1/3, 5/9, and 7/9 plateaus are David-star sqrt(3)xsqrt(3) VBCs, that local magnetization is always strongly inhomogeneous below saturation, and that the 1/9 plateau observed in YCOB should be interpreted as a VBC rather than a chiral spin liquid.

Significance. If the reported energies are converged, the paper offers a concrete resolution of a long-standing controversy about the 1/9 plateau. A strength is that the general RVB ansatz explicitly contains the NN-U(1) ansatz of Ref. 17 as a subset, so the lower variational energy is a genuine improvement over that specific prior state and is not circular. The finite-depth BFGS algorithm is also a practical methodological advance for optimizing ~6.6e5 variational parameters, where the full stochastic-reconfiguration matrix would be unmanageable. The paper makes explicit, falsifiable predictions, such as reversed local magnetization at the 1/9 plateau and strong spatial inhomogeneity of the magnetic response, which could be probed by NMR or torque measurements. However, the quantitative claims are not yet reproducible: no Monte Carlo sample counts, statistical errors, optimizer hyperparameters, or data/code availability are provided, and the central energy gap of 0.0068 J/site is quoted as a bare number.

major comments (5)
  1. [§IV A, Eq. (24)] The central energy comparison (E = -0.4184 vs -0.4116/-0.4111 J/site) is presented without statistical uncertainties. The energy is evaluated by Monte Carlo sampling of Eq. (24), but the paper gives no sample count, autocorrelation time, or standard error, and no convergence criterion for the finite-depth BFGS optimizer (restart depth K, step size delta, number of iterations). Since the claimed gap is only 0.0068 J/site, about 1.6% of the total energy, the claim that the windmill VBC is significantly lower cannot be verified as written. Please report standard errors and convergence diagnostics for the 1/9 plateau energies on both clusters.
  2. [§IV B 3; §V] The comparison with the Z3 chiral spin liquid is not fully controlled. Because the NN-U(1) ansatz of Ref. 17 is a subset of the general ansatz, obtaining an energy below -0.4116 is a legitimate variational improvement over that specific state. However, the paper's broader conclusion that the 1/9 plateau state is not a Z3 chiral spin liquid requires excluding chiral states inside the general variational family. The manuscript never seeds the optimization with a Z3 chiral initial condition, nor does it re-optimize a chiral state after adding longer-range terms. Such a test, or an explicit restriction of the conclusion to the specific NN-U(1) chiral state, is needed.
  3. [§IV B 3, Fig. 5] The windmill VBC is obtained after 'induced optimization' in which exchange couplings are strengthened on selected rings, which is an explicit symmetry-breaking seed. The manuscript does not specify the strength or duration of the induced stage, nor does it demonstrate that the relaxed state is a local minimum of the original Hamiltonian rather than a basin artifact. Given the authors' statement that the 1/9 plateau VBC energy gain is 'much shallower' than at the 1/3 plateau, the relaxation process should be documented with energy traces and with a comparison to unseeded optimization on the same cluster.
  4. [§IV A, Fig. 3, Table I] The thermodynamic-limit claim rests on only two cluster sizes (N=108 and N=432), and the paper itself states that finite-size effects are 'still very strong' in the magnetization curve. No explicit per-site energies at the 1/9 magnetization (M/N = 1/9) are tabulated for the two clusters, and no extrapolation in 1/N is shown. Please provide the energies for both clusters at the plateau magnetization and an estimate of the thermodynamic limit before asserting that the N=432 cluster is 'large enough'.
  5. [§II, Eq. (7)] The variational state is a single Gutzwiller-projected BCS/Slater-determinant wave function. Although long-range hopping and pairing parameters make it very flexible, multi-determinant superpositions and alternative parton constructions are excluded by construction. The abstract's phrase 'most general variational ansatz based on the RVB picture' therefore overstates the variational space, and the conclusions about the true ground state in Sec. V are conditional on this single-determinant family. This limitation should be stated explicitly when the ansatz is introduced.
minor comments (4)
  1. [§IV A] The word 'Mysteriously' in the comparison of the previous variational and tensor-network energies is not appropriate in a scientific report and should be removed or rephrased.
  2. [§IV B 4, Eq. (36)] The scaling sigma_m proportional to sqrt(m) in the small-m limit is stated without showing a fit, the fitted range, or the data points; please provide this information or soften the claim.
  3. [Fig. 5] The lower panel, meant to show the detailed distribution of local magnetization and spin correlations in the 27-site unit cell, is difficult to read in the printed version; a table of the site-resolved values would make the windmill pattern reproducible.
  4. [References] Several references contain apparent formatting errors or missing fields, including the 'ZnCu3(OH)6FrBr' formula in Ref. 26 and the incomplete journal information in Ref. 30; these should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the variational energy comparison is a genuine superset optimization, and the windmill VBC pattern is not a fitted input to the Hamiltonian.

full rationale

The paper's central derivation is a variational energy minimization over a general fermionic RVB ansatz (Eqs. 4, 7, 22-24). The comparison to the Z3 chiral spin liquid of Ref. 17 is a genuine variational improvement rather than a restatement of an input: the authors' HMF contains the NN-U(1) ansatz as a parameter subset, so optimizing over the larger family can only lower the energy. The windmill VBC energy (-0.4184 J/site) is obtained from an independently optimized variational state, and no measured or previously claimed plateau energy is used to set any variational parameter. The magnetization curve and the local-magnetization inhomogeneity are read out from the optimized state, not fitted to the target plateaus. The finite-depth BFGS algorithm is attributed to the authors' prior work (Ref. 32), but the update rule is fully specified in Sec. III and is a numerical method rather than load-bearing physical evidence; Ref. 35 is used only as a supporting analogy. The induced-optimization procedure seeds a pattern and then relaxes under the original Hamiltonian, so the final energy is still a variational energy of the true model. Concerns about whether the BFGS run reached the global minimum, whether the Z3 state was re-optimized within the general ansatz, and the absence of statistical error bars are correctness and verification risks, not circularity. No derivation step reduces to its own input by construction.

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

The variational parameters (U matrix elements, related to chi and Delta) are the free parameters of the calculation; the physical conclusion (which VBC pattern wins) is a function of their optimized values. The induced-optimization step adds a hand-chosen bias, and the BFGS hyperparameters are unspecified algorithmic free choices. No new particles or fields are introduced. The central axiom is that the projected single-Slater-determinant family is large enough to contain the true ground state; this is the main structural limitation of the result.

free parameters (3)
  • General RVB variational parameters (matrix elements of U related to chi and Delta) = not reported; N_v = 663,552 at m=1/9 on N=432 cluster
    All hopping and pairing amplitudes are optimized to minimize the variational energy; the final values determine the VBC pattern, so the claim rests on these fitted numbers.
  • Induced-optimization bond strengthening factor = not specified
    During the induction step the exchange coupling on selected motifs is artificially increased; the relaxed state's energy is said to be lower, but the choice of which bonds to strengthen is a hand-chosen input.
  • BFGS optimizer hyperparameters (restart depth K, step size delta) = not specified
    These affect which local minimum is reached; the manuscript gives no values, making reproducibility impossible without further details.
assumptions (3)
  • domain assumption The true ground state at the 1/9 plateau is well approximated by a single Gutzwiller-projected fermionic Slater determinant (RVB state).
    The variational calculation is restricted to this family; states outside it, such as multi-determinant superpositions or other parton constructions, are excluded. The authors call the ansatz 'most general' within the RVB picture, but that is not equivalent to all possible quantum states.
  • domain assumption Clusters with L a multiple of 3 and periodic boundary conditions are sufficient to capture the competing VBC orders.
    Only N=108 and N=432 clusters are used; no other shapes or boundary conditions are tested, so the stability of the windmill pattern against finite-size and boundary effects is not established.
  • standard math Spin inversion symmetry can be used to reduce the variational parameter count without loss of generality.
    The mapping M to -M is a symmetry of the Hamiltonian; using it to halve the parameter count is valid provided the optimized state does not spontaneously break this symmetry in a way that is missed.

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Cite this review

Pith. "Pith review of Variational study of the magnetization plateaus of the spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet and its implication on YCOB." pith.science (2026). https://pith.science/paper/57C55OZC

@misc{pith2026250720308,
  author       = {Pith},
  title        = {Pith review of: Variational study of the magnetization plateaus of the spin-$\frac12$ kagome Heisenberg antiferromagnet and its implication on YCOB},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/57C55OZC}},
  note         = {Machine review of arXiv:2507.20308}
}
abstract

Numerical simulations find that there are multiple plateaus in the magnetization curve of the spin-$\frac{1}{2}$ Kagome antiferromagnetic Heisenberg model(KAFH) at fractional magnetization $m=1/9,1/3,5/9,7/9$. While it is well known that the $m=1/3,5/9,7/9$ plateau feature a $\sqrt{3}\times\sqrt{3}$ valence bond crystal(VBC) ordering pattern with a David-star-shaped motif, the origin of the narrow plateau at $m=1/9$ remains elusive. Some researchers claim that a subtle translational symmetry breaking pattern with the same $\sqrt{3}\times\sqrt{3}$ periodicity occurs at the $m=1/9$ plateau. On the other hand, it has also been argued that the $m=1/9$ plateau may harbor a novel $Z_{3}$ chiral spin liquid phase. To resolve this controversy, we have proposed the most general variational ansatz based on the resonating valence bond(RVB) picture that is consistent with the spin symmetry of the system and developed a new algorithm to optimize such a complicated ansatz. We find that a peculiar VBC state with a $3\times3$ periodicity and a windmill-shaped motif has significantly lower energy than the claimed $Z_{3}$ chiral spin liquid state and other proposed VBC states around the $m=1/9$ plateau. We find that there are strong spatial modulation in the local magnetization at the $1/9$ plateau, so strong that even its polarization can be reversed. Our general RVB ansatz also well reproduces all other more conventional magnetization plateaus of the spin-$\frac{1}{2}$ KAFH. We find that the local magnetization is always strongly inhomogeneous below the saturating field for such a strongly frustrated quantum magnet.

Figures

Figures reproduced from arXiv: 2507.20308 by the authors.

Figure 1
Figure 1. FIG. 1: Illustration of the kagome cluster on which our vari [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: (a)Overlay of the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4: The [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Fig.5. We note that reversal of polarization in the local [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Upper panel: The 3 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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Works this paper leans on

35 extracted references · 33 canonical work pages

  1. [1]

    E. F. Shender, Antiferromagnetic garnets with fluctuationally interacting sublattices, Sov. Phys. JETP, 56, 178(1982)

    work page 1982

  2. [2]

    Kawamura, Spin wave analysis of the antiferromagnetic plane rotator model on the triangular lattice - symmetry breaking in a magnetic field, J.Phys.Soc.Jpn

    H. Kawamura, Spin wave analysis of the antiferromagnetic plane rotator model on the triangular lattice - symmetry breaking in a magnetic field, J.Phys.Soc.Jpn. 53, 2452(1984)

    work page 1984

  3. [3]

    A. V. Chubukov and D. I. Golosov, Quantum theory of an antiferromagneton a triangular lattice in a magnetic field, J. Phys.: Condens.Matter 3 69( 1991)

    work page 1991

  4. [4]

    Hida, Magnetization process of the S=1 and 1/2 uniform and distorted kagome Heisenberg antiferromagnets

    K. Hida, Magnetization process of the S=1 and 1/2 uniform and distorted kagome Heisenberg antiferromagnets. J. Phys. Soc. Jpn 70, 3673(2001)

    work page 2001

  5. [5]

    Richter, J

    Honecker, A., Schulenburg, J. Richter, J. Magnetization plateaus in frustrated antiferromagnetic quantum spin models. J. Phys. Condens. Matter 16, S749(2004)

    work page 2004

  6. [6]

    Zhitomirsky and H

    M.E. Zhitomirsky and H. Tsunetsugu, Exact low temperature behavior of a kagome antiferromagnet at high fields, Phys. Rev. B 70, 100403(R) (2004)

    work page 2004

  7. [7]

    Nakano and T

    H. Nakano and T. Sakai, Magnetization process of kagome lattice Heisenberg antiferromagnet, J. Phys. Soc. Jpn. 79, 053707 (2010)

    work page 2010

  8. [8]

    Sakai and H

    T. Sakai and H. Nakano, Critical magnetization behavior of the triangular and kagome lattice quantum antiferromagnets, Phys. Rev. B 83, 100405(R) (2011)

    work page 2011

Show all 35 references
  1. [9]

    Nishimoto, N

    S. Nishimoto, N. Shibata, and C. Hotta, Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet, Nat. Commun. 4, 2287 (2013)

    2013

  2. [10]

    Capponi, O

    S. Capponi, O. Derzhko, A. Honecker, A. M. Läuchli, and J. Richter, Numerical study of magnetization plateaus in the spin-1/2 kagome Heisenberg antiferromagnet, Phys. Rev. B 88, 144416 (2013)

    2013

  3. [11]

    Picot, M

    T. Picot, M. Ziegler, R. Orus, and D. Poilblanc, Spin-S kagome quantum antiferromagnets in a field with tensor networks, Phys. Rev. B 93, 060407(R) (2016)

    2016

  4. [12]

    Schnack, J

    J. Schnack, J. Schulenburg, A. Honecker, and J. Richter, Magnon crystallization in the kagome lattice antiferromagnet, Phys. Rev. Lett. 125, 117207 (2020)

    2020

  5. [13]

    Oshikawa, M

    M. Oshikawa, M. Yamanaka and I. Affleck, Magnetization plateaus in spin chains; ‘‘Haldane gap’’ for half-integer spins. Phys. Rev. Lett. 78, 1984 (1997)

    1997

  6. [14]

    D. Z. Fang, N. Xi, S.-J. Ran, and G. Su, Nature of the 1/9-magnetization plateau in the spin-1/2 kagome Heisenberg antiferromagnet, Phys. Rev. B 107, L220401 (2023)

    2023

  7. [15]

    Hotta and N

    C. Hotta and N. Shibata, Grand canonical finite-size numerical approaches: A route to measuring bulk properties in an applied field, Phys. Rev. B 86, 041108 (2012)

    2012

  8. [16]

    Hotta, S

    C. Hotta, S. Nishimoto and . Shibata, Grand canonical finite size numerical approaches in one and two dimensions: real space energy renormalization and edge state generation. Phys. Rev. B 87, 115128 (2013)

    2013

  9. [17]

    He, S.-L

    L.-W. He, S.-L. Yu, and J.-X. Li, Variational monte carlo study of the 1/9-magnetization plateau in kagome antiferromagnets, Phys. Rev. Lett. 133, 096501 (2024)

    2024

  10. [18]

    Morita, Valence bond crystal ground state of the 1/9 magnetization plateau in the spin-1/2 kagome lattice, J

    K. Morita, Valence bond crystal ground state of the 1/9 magnetization plateau in the spin-1/2 kagome lattice, J. Phys. Soc. Jpn. 93, 123706 (2024)

    2024

  11. [19]

    Chen, Y.-X

    X.-H. Chen, Y.-X. Huang, Y. Pan, and J.-X. Mi, Quantum spin liquid candidate YCu _ 3 (OH) _ 6 Br _ 2 [Br _ x (OH) _ 1-x ]( x 0.51 ): with an almost perfect kagome layer, J. Magn. Magn. Mater. 512, 167066 (2020)

    2020

  12. [20]

    J. Liu, L. Yuan, X. Li, B. Li, K. Zhao, H. Liao, and Y. Li, Gapless spin liquid behavior in a kagome Heisenberg antiferromagnet with randomly distributed hexagons of alternate bonds, Phys. Rev. B 105, 024418 (2022)

    2022

  13. [21]

    Z. Zeng, X. Ma, S. Wu, H.-F. Li, Z. Tao, X. Lu, X.-h. Chen, J.-X. Mi, S.-J. Song, G.-H. Cao, G. Che, K. Li, G. Li, H. Luo, Z. Y. Meng, and S. Li, Possible Dirac quantum spin liquid in the kagome quantum antiferromagnet YCu _ 3 (OH) _ 6 Br _ 2 [Br _ x (OH) _ 1-x ], Phys. Rev. B...

    2022

  14. [22]

    F. Lu, L. Yuan, J. Zhang, B. Li, Y. Luo, and Y. Li, The observation of quantum fluctuations in a kagome Heisenberg antiferromagnet, Commun. Phys. 5, 272 (2022)

    2022

  15. [23]

    Mendels, F

    P. Mendels, F. Bert, M. A. de Vries, A. Olariu, A. Harrison, F. Duc, J. C. Trombe, J. S. Lord, A. Amato, and C. Baines, Quantum magnetism in the paratacamite family: towards an ideal kagome lattice, Phys. Rev. Lett. 98 077204(2007)

    2007

  16. [24]

    J. S. Helton, K. Matan, M. P. Shores, E. A. Nytko, B. M. Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu, J. H. Chung, D. G. Nocera, and Y. S. Lee, Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu _ 3 (OH) _ 6 Cl _ 2 , Phys. Rev. Lett. 98 107204(2007)

    2007

  17. [25]

    T. H. Han, J. S. Helton, S. Chu, D. G. Nocera, J. A. Rodriguez Rivera, C. Broholm, and Y. S. Lee, Fractionalized excitations in the spin liquid state of a kagome lattice antiferromagnet, Nature 492 406(2012)

    2012

  18. [26]

    Z. L. Feng, Z. Li, X. Meng, W. Yi, Y. Wei, J. Zhang, Y. C. Wang, W. Jiang, Z. Liu, S. Y. Li, F. Liu, J. L. Luo, S. L. Li, G. Q. Zheng, Z. Y. Meng, J. W. Mei and Y. G. Shi, Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu _ 3 Zn(OH) _ 6 FBr, Ch...

    2017

  19. [27]

    S. Jeon, D. Wulferding, Y. Choi, S. Lee, K. Nam, K. Kim, M. Lee, T.-H. Jang, J.-H. Park, S. Lee, S. Choi, C. Lee, H. Nojiri, and K. Choi, One-ninth magnetization plateau stabilized by spin entanglement in a kagome antiferromagnet, Nat. Phys. 20, 1(2024)

    2024

  20. [28]

    Suetsugu, T

    S. Suetsugu, T. Asaba, Y. Kasahara, Y. Kohsaka, K. Totsuka, Boqiang Li, Yuqiang Zhao, Yuesheng Li, M. Tokunaga, and Y. Matsuda, Emergent spin-gapped magnetization plateaus in a spin-1/2 perfect kagome antiferromagnet. Phys. Rev. Lett. 132, 226701(2024)

    2024

  21. [29]

    Zheng, Y

    G. Zheng, Y. Zhu, K.-W.Chen, B. Kang, D. Zhang, K. Jenkins, A. Chan, Z. Zeng, A. Xu, O.A. Valenzuela, J. Blawat, J. Singleton, P. A. Lee, S. Li, and L. Li, Unconventional magnetic oscillations in a kagome Mott insulator, PNAS, 122, e2421390122(2025)

    2025

  22. [30]

    Suetsugu, T

    S. Suetsugu, T. Asaba, S. Ikemori, Y. Sekino, Y. Kasahara, K. Totsuka, B. Li, Y. Zhao, Y. Li, Y. Kohama, and Y. Matsuda, Gapless spin excitations in a quantum spin liquid state of s=1/2 perfect kagome antiferromagnet (2024), arXiv:2407.16208

    2024 arXiv

  23. [31]

    Zheng, D

    G. Zheng, D. Zhang, Y. Zhu, K.-W. Chen, A. Chan, K. Jenkins, B. Kang, Z. Zeng, A. Xu, D. Ratkovski, J. Blawat, A. Bangura, J. Singleton, P. A. Lee, S. Li, and L. Li, Thermodynamic evidence of fermionic behavior in the vicinity of one-ninth plateau in a kagome antiferromagnet (...

    2024

  24. [32]

    Jian-Hua Yang and Tao Li, Instability of the U (1) spin liquid with a large spinon Fermi surface in the Heisenberg-ring exchange model on the triangular lattice, Phys. Rev. B 108, 235105(2023)

    2023

  25. [33]

    Sorella, Two spin liquid phases in the spatially anisotropic triangular Heisenberg model, Phys

    S.Yunoki and S. Sorella, Two spin liquid phases in the spatially anisotropic triangular Heisenberg model, Phys. Rev. B 74, 014408 (2006)

    2006

  26. [34]

    Nocedal and S

    J. Nocedal and S. J. Wright, Numerical \ Optimization , Springer(2008)

    2008

  27. [35]

    Jian-Hua Yang and Tao Li, Strong relevance of zinc impurities in spin-1/2 kagome quantum antiferromagnets: A variational study, Phys. Rev. B 109, 115103(2024)

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.