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Wannier states and spin supersolid physics in the triangular antiferromagnet K$_2$Co(SeO$_3$)$_2$

T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper argues that the triangular-lattice antiferromagnet K2Co(SeO3)2 is a spin supersolid whose low-energy excitations form a continuum driven by strong quantum fluctuations rather than coherent magnons.

desk verdict Strong experimental follow-up: the zero-field supersolid evidence is solid, but the finite-field QMC agreement is less controlled than advertised and should be softened. read the letter →

arxiv 2412.19693 v2 pith:5NSVBMQ6 submitted 2024-12-27 cond-mat.str-el

M. Zhu , Leandro M. Chinellato , V. Romerio , N. Murai , S. Ohira-Kawamura , Christian Balz , Z. Yan , S. Gvasaliya
show 3 more authors
Yasuyuki Kato C. D. Batista A. Zheludev
This is my paper · ORCID
classification cond-mat.str-el
keywords spinsupersolidtriangularlatticeXXZmodelWannierstatesinelasticneutronscatteringquantumMonteCarloexcitationcontinuumpseudo-Goldstonemode
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

The paper argues that K2Co(SeO3)2 is a near-ideal realization of a spin supersolid: its layers of cobalt spins order in a Y-shaped pattern while their transverse components carry superfluid-like phase coherence, in the language of the hard-core-boson mapping. Ultra-high-resolution neutron scattering resolves no discrete magnon modes inside a broad low-energy continuum, and thermodynamic measurements recover the 0.323R Wannier entropy of the parent triangular Ising model. Quantum Monte Carlo simulations of the projected low-energy model reproduce the magnetization, specific heat, entropy, and the zz component of the spin spectrum. The authors conclude that the continuum emerges from strong quantum fluctuations within the Wannier subspace, not from semiclassical spin-wave physics. If correct, this material offers a quantitative testbed for strongly quantum frustrated magnetism.

What carries the argument

The argument runs through the Wannier subspace W of the triangular Ising model: spin configurations in which no elementary triangle has all three spins parallel. This subspace is macroscopically degenerate, with residual entropy 0.323R, and projecting the XXZ Hamiltonian onto it yields a quantum dimer model with a ring-exchange term on the dual honeycomb lattice. A unitary transformation reverses the sign of the Jxy term without changing the spectrum or the Sz correlations, eliminating the sign problem and making large-scale quantum Monte Carlo simulations possible. The dimer-resonance dynamics inside W is what generates the low-energy continuum, the roton-like dips, and the pseudo-Goldstone gap.

What would settle it

If a spectrometer with energy resolution below 23 micro-eV resolved the low-energy continuum into discrete magnon branches at the M point or elsewhere on the zone boundary, the intrinsic-quantum-continuum claim would be wrong. Alternatively, a quantum Monte Carlo calculation that includes the neglected second-order Jxy terms and loses agreement with specific heat, entropy, and magnetization at finite field would falsify the effective-model route.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that K2Co(SeO3)2 exhibits a spin-supersolid phase described by a nearest-neighbor XXZ Hamiltonian with Jzz = 3.1 meV and Jxy/Jzz = 0.07. At zero field the system shows three BKT-type transitions, an entropy plateau at the Wannier value, a gapless Goldstone mode, a 0.06 meV pseudo-Goldstone mode, and continua of excitations where the Ising model would place flat spin-flip bands. In a magnetic field the continuum progressively sharpens into coherent spin waves as the system approaches the 1/3 up-up-down plateau at about 0.8 T, with the Goldstone and pseudo-Goldstone branches responding differently. The authors state that, at the studied energy scales, one can conclude with reasonable confidence that the material realizes the spin-supersolid phase.

Load-bearing premise

The load-bearing premise is that projecting the full XXZ Hamiltonian onto the Wannier subspace and dropping second-order terms in Jxy remains accurate at finite fields up to 0.5 T, even though the sign-reversing mapping that makes the quantum Monte Carlo algorithm work is proven exact only in the Ising limit at zero field.

Editorial extensions

If this is right

  • If correct, K2Co(SeO3)2 becomes a concrete material where spin-supersolid order and strongly quantum dynamics coexist, not just a numerical prediction.
  • Semiclassical linear spin-wave theory fails to describe the zero-field spectrum; any successful description must reproduce the broad continuum and its sharp lower-boundary feature.
  • The field evolution of the pseudo-Goldstone gap (0.06 to 0.16 to 0.26 meV) and the differing fate of the two roton dips provide a fingerprint for distinguishing competing theoretical scenarios.
  • The high-energy 3 meV spin-flip continuum replaces the flat Ising band, and its broadening directly measures quantum fluctuations within the Wannier manifold.
  • The sign-free quantum Monte Carlo route validated here can be used to predict further observables of the same effective dimer model in the supersolid phase.

Reading between the lines

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

  • I would extend the paper's analysis by noting that the missing M-point continuum in the QMC Szz channel suggests that the transverse Sxx and Syy channels carry a large share of the spectral weight; polarized neutron scattering could test this directly.
  • The paper deliberately leaves open whether the continuum is fractionalized spinon-like scattering or unresolved closely spaced magnon modes; scanning the continuum edge with even finer energy resolution at selected wave vectors would be the natural discriminator.
  • The same Wannier-subspace projection should apply to other strongly Ising-like triangular magnets with anisotropy ratio below roughly 0.1; the paper explicitly rules out Na2BaCo(PO4)2 with its larger ratio, so a testable prediction is that continuum-dominated supersolid dynamics is confined to the deep-Ising regime.
  • The 'spin supersolid' label is used by analogy through the hard-core-boson mapping, and the paper itself notes that real spin systems lack a conserved spin current; the robust content of the claim is therefore quantum dynamics in a symmetry-broken easy-axis magnet rather than literal superfluidity.
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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

2 major / 5 minor

Summary. This manuscript combines ultra-high-resolution inelastic neutron scattering, thermodynamic measurements, and quantum Monte Carlo (QMC) simulations of an effective XXZ model to argue that the triangular-lattice antiferromagnet K2Co(SeO3)2 realizes a spin-supersolid phase described by a nearest-neighbor XXZ Hamiltonian with strong easy-axis anisotropy. The experimental highlights include a Wannier entropy plateau at 0.323R, two BKT-type specific-heat anomalies at zero field, a low-energy excitation continuum in which no discrete magnons are resolved down to 23 \mu eV resolution, a 0.06 meV pseudo-Goldstone gap at the K point, and a higher-energy continuum near 3 meV. Under applied fields the continuum evolves into sharper spin-wave-like excitations as the system approaches the 1/3 uud plateau. QMC results for magnetization, specific heat, entropy, and the S_zz component of the dynamical structure factor are compared with experiment, and the paper concludes that the material hosts a spin supersolid with strongly quantum dynamics.

Significance. If the conclusions hold, this is one of the most complete experimental and numerical characterizations of a spin supersolid in a frustrated magnet. The experimental achievements are substantial: the 23 \mu eV resolution, the recovery of the Wannier entropy, and the resolution of a 60 \mu eV pseudo-Goldstone gap set a new standard for studying near-Ising triangular antiferromagnets. The numerical work is also valuable, combining sign-problem-free QMC with first-pole extraction and analytic continuation. The paper does not claim to determine the microscopic nature of the continuum, but it places severe constraints on semiclassical magnon scenarios and frames a clear set of questions for future theory. However, as detailed below, the finite-field QMC route contains an uncontrolled approximation, and part of the parameter validation is circular; these issues need to be addressed before the quantitative agreement can be regarded as a fully independent test of the model.

major comments (2)
  1. [Section II.E and II.F] The QMC comparison at finite fields rests on an uncontrolled approximation. The unitary transformation that reverses the sign of Jxy is constructed in the zero-field Wannier subspace, and Section II.F itself states that the mapping is exact only in the Ising limit and at zero field. Nevertheless, QMC results at \mu_0H = 0.25 and 0.5 T are compared with experiment in Figs. 12, 16, 17, and 18. The neglected second-order Jxy processes have an energy scale Jxy^2/Jzz \approx (0.217)^2/3.1 meV \approx 0.015 meV, which is not negligible compared with the 0.06 meV pseudo-Goldstone gap used as a key fingerprint. The paper gives no quantitative estimate of these corrections or of the weight of states outside the Wannier subspace at finite field. I recommend adding a small-cluster exact-diagonalization benchmark (or a variational estimate) of the projected effective model versus the full Hamiltonian at finite field, and a discussion of how the second-order corrections affect the first poles and the pseudo-Goldstone gap. Without such a test, the excellent agreement in Figs. 12 and 16-18 could be coincidental rather than a validation of the XXZ description.
  2. [Section II.D and II.F] Part of the validation loop is circular. The text states that Jzz = 3.1 meV and Jxy = 0.217 meV were further refined by detailed comparison with theoretical calculations, and that this refinement was essential to achieve agreement with the specific heat and magnetization curves. The QMC simulations then reproduce those same specific heat and magnetization curves (Figs. 12, 16, 17), making that portion of the agreement a consistency check rather than an independent prediction. The genuinely independent content comes from the spectral observables: first poles, continuum shape, and the field splitting of the pseudo-Goldstone mode. The manuscript should explicitly separate fitted from predicted observables and, ideally, show the sensitivity of the predicted spectral features to variations of Jxy and Jzz within the range allowed by magnetometry.
minor comments (5)
  1. [Section II.C and Fig. 6] The QMC spectral lines are normalized by an arbitrary global factor chosen at the M point; the figures therefore demonstrate shape agreement rather than absolute intensity agreement. This should be stated in the main text whenever spectral intensities are discussed.
  2. [Section II.F] The sentence 'The lowest temperature reached by QMC calculations is slightly higher than the experimental value (T = 0.12 K)' is ambiguous, because the experimental data are reported down to 0.12 K. Please clarify which temperature floor is meant for the QMC data and for the experimental data.
  3. [Section II.B and Fig. 16] The nuclear Schottky subtraction is determined at zero field (\Delta = 0.084 K), but the same subtraction appears to be applied to the finite-field specific-heat data in Fig. 16. If the Schottky term is field-dependent, this introduces a small systematic error at the lowest temperatures; the authors should either estimate the field dependence or state explicitly that it is neglected.
  4. [Methods] The QMC code is only available upon reasonable request, while the analysis tools (Sunny.jl, SmoQyDEAC.jl) are public. For reproducibility, consider depositing the modified QMC code in a public repository.
  5. [Throughout] There are several typographical errors, including 'antiferro magnet' in the title and 'backbround' in the caption of Fig. 11; these should be corrected during revision.

Circularity Check

1 steps flagged · score 3.0 of 10

Thermodynamic 'validation' is a consistency check because Jzz and Jxy were refined to match those curves; the spectral conclusions remain independent.

  1. fitted input called prediction [Sec. II.D (Hamiltonian model), after Eq. (1); compared with Sec. II.F (QMC simulations)]
    "The exchange interactions determined in [33] through high-field magnetometry measurements were further refined by detailed comparison with theoretical calculations, as discussed below. This process yielded updated values of Jzz = 3.1 meV, Jxy = 0.217 meV, and an anisotropy ratio of α = Jxy/Jzz = 0.07. The refinement was essential to achieve a precise agreement with the specific heat and magnetization curves presented in subsequent sections."

    The QMC section then presents agreement with exactly these curves as model validation: 'To further validate the proposed spin Hamiltonian and the low-energy model derived in the previous section, we computed the uniform magnetization curve M(µ0H)... the calculated magnetization curve is in good agreement with the experimental data, predicting a critical field...'. Because Jzz and Jxy were explicitly refined to match the same specific-heat and magnetization curves, the QMC reproduction of those curves is a consistency check of the fitting loop rather than an independent prediction.

full rationale

The paper candidly describes the model-determination loop as 'ouroboric', and one genuine circular step exists: the Hamiltonian parameters are refined to match the specific heat and magnetization curves, and those same curves are later presented as QMC validation. This is a fitted-input-called-prediction issue, but it is confined to the thermodynamic support. The sign-reversing unitary transformation is taken from independent prior work ([29], [30], [52]), not from an unpublished self-citation; the QMC code is checked against exact diagonalization; and the key spectral benchmarks (60 µeV pseudo-Goldstone gap, continuum weight, roton dips, finite-field splitting) are not used as fit targets. The central claim of a Y-type spin supersolid with strongly quantum low-energy dynamics therefore rests on comparisons that are not forced by the parameter fit. The finite-field use of a mapping stated to be exact only in the Ising limit at zero field is a serious correctness risk, but it is an uncontrolled-approximation concern rather than a definitional circularity. Overall score 3: partial circularity in the thermodynamic validation, with independent content in the spectral derivation.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central model has five fitted inputs, mostly material parameters refined against thermodynamic data. The Wannier space and dimer-covering representation are mathematical re-formulations of the known Ising ground-state manifold, not new physical entities. No new particles, forces, or conserved quantities are introduced.

free parameters (5)
  • Jzz = 3.1 meV
    Out-of-plane exchange coupling, originally from high-field magnetometry (Ref 33) and later refined to match specific heat and magnetization curves (Section II.D).
  • Jxy = 0.217 meV
    In-plane exchange coupling, refined to reproduce the specific heat and magnetization data; sets the energy scale of the low-energy theory and the pseudo-Goldstone gap scale.
  • gzz = 7.9
    z-component of the Lande g-tensor, used to convert applied magnetic field to Zeeman energy; taken from magnetometry, not independently derived here.
  • Schottky splitting Delta = 0.084(1) K
    Fitted to the low-temperature nuclear Schottky upturn in heat capacity; the subtraction affects the extracted magnetic entropy and transition temperatures.
  • Phonon scale factor = 1.08
    Empirical scale factor matching K2Mg(SeO3)2 heat capacity to K2Co(SeO3)2 in the range 50-100 K; used for phonon subtraction.
assumptions (5)
  • standard math Wannier's exact solution of the triangular Ising model, including the macroscopically degenerate ground states, residual entropy 0.323R, and flat single-spin-flip bands at nJzz.
    Background exact result from Ref 22, used to identify the Wannier entropy plateau and the high-energy spin-flip continuum.
  • domain assumption The unitary transformation U = exp(i pi N_s/2) maps Heff to -Heff, removing the sign problem while preserving the spectrum and S^z correlation functions (Refs 29,30).
    Cited mathematically from prior literature; it is the basis for the sign-problem-free QMC approach.
  • ad hoc to paper Projection onto the Wannier subspace with neglect of second-order Jxy corrections is valid for alpha = 0.07.
    The authors state they "bypass this difficulty by solving the non-frustrated XXZ Hamiltonian and neglecting second-order corrections in Jxy," and later note the mapping is exact only in the Ising limit and at zero field (Sections II.E, II.F).
  • domain assumption A nearest-neighbor XXZ Hamiltonian with no additional interactions describes the material.
    The Discussion says additional interactions cannot be completely ruled out, but are assumed weak at the studied energy scales.
  • domain assumption Measured neutron intensity is dominated by the S_zz component because gzz/g_xy is approximately 4.
    This is a crude estimate from Curie-Weiss susceptibility (Section II.C); if it fails, the S_zz-only QMC comparison is incomplete.

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Cite this review

Pith. "Pith review of Wannier states and spin supersolid physics in the triangular antiferromagnet K$_2$Co(SeO$_3$)$_2$." pith.science (2026). https://pith.science/paper/5NSVBMQ6

@misc{pith2026241219693,
  author       = {Pith},
  title        = {Pith review of: Wannier states and spin supersolid physics in the triangular antiferromagnet K$_2$Co(SeO$_3$)$_2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5NSVBMQ6}},
  note         = {Machine review of arXiv:2412.19693}
}
abstract

We combine ultra-high-resolution inelastic neutron scattering and quantum Monte Carlo simulations to study thermodynamics and spin excitations in the spin-supersolid phase of the triangular lattice XXZ antiferromagnet K$_2$Co(SeO$_3$)$_2$ under zero and non-zero magnetic field. BKT transitions signaling the onset of Ising and supersolid order are clearly identified, and the Wannier entropy is experimentally recovered just above the supersolid phase. At low temperatures, with an experimental resolution of about 23 $\mu$eV, no discrete coherent magnon modes are resolved within a broad scattering continuum. Alongside gapless excitations, a pseudo-Goldstone mode with a 0.06 meV gap is observed. A second, higher-energy continuum replaces single-spin-flip excitations of the Ising model. Under applied fields, the continuum evolves into coherent spin waves, with Goldstone and pseudo-Goldstone sectors responding differently. The experiments and simulations show excellent quantitative agreement.

Figures

Figures reproduced from arXiv: 2412.19693 by the authors.

Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 3
Figure 3. (a) shows the zero-field specific heat of K2Co(SeO3)2 measured up to high temperatures (open circles). The phonon contribution is approximated by the measured specific heat of the isostructural nonmagnetic counterpart K2Mg(SeO3)2 (solid squares). An empirical scale factor of 1.08 was applied in order to match the heat capacities of the two systems in the temperature range 50−100 K. The upturn below 0.2 K [42] is asc… view at source ↗
Figures from the paper (13 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 5
Figure 5. Figure 5: To better understand the nature of the low-energy continuum of excitations in the supersolid phase of K2Co(SeO3)2, we have investigated their evolution in a magnetic field applied along the magnetic easy axis (i.e. c axis) at LET. In [PITH_FULL_IMAGE:figures/full_fig_…
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p009_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13 [PITH_FULL_IMAGE:figures/full_fig_p010_13.png]
Figure 15
Figure 15. Figure 15: FIG. 15 [PITH_FULL_IMAGE:figures/full_fig_p011_15.png]
Figure 14
Figure 14. Figure 14: FIG. 14 [PITH_FULL_IMAGE:figures/full_fig_p011_14.png]
Figure 16
Figure 16. Figure 16: FIG. 16 [PITH_FULL_IMAGE:figures/full_fig_p012_16.png]
Figure 17
Figure 17. Figure 17: FIG. 17 [PITH_FULL_IMAGE:figures/full_fig_p012_17.png]
Figure 18
Figure 18. Figure 18: presents QMC simulations for µ0H = 0, 0.25, and 0.5 T. The white dots indicate the lowest en￾ergy pole (first pole) of the DSSF extracted from the QMC data as presented in Methods. Since the QMC simulations are performed in imaginary time, an analytic continuation is …

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

  1. The anisotropic Heisenberg model close to the Ising limit: triangular lattice vs. effective models

    cond-mat.str-el 2025-10 conditional novelty 4.0 of 10

    DMRG and exact-diagonalization results on up to 72 sites indicate a gapped zero-field ground state for the easy-axis triangular-lattice Heisenberg model with α≲0.3–0.5, and a crossover/transition to gapless behavior a...

Reference graph

Works this paper leans on

86 extracted references · 59 canonical work pages · cited by 1 Pith paper

  1. [1]

    and shows qualitative consistency with the predictions of previous studies [ 45, 46, 50, 51]. Up to this point, we have presented arguments, sup- ported by both the current literature and our experi- mental data, demonstrating that K 2Co(SeO3)2 is well described by the XXZ Hamiltonian (Eq. 1). Specifically, we highlighted that LSWT accurately captures the ...

    work page

  2. [2]

    superfluid

    A. J. Leggett, Can a solid be “superfluid”?, Phys. Rev. Lett. 25, 1543 (1970)

    work page 1970

  3. [3]

    A. F. Andreev and I. M. Lifshitz, Quantum theory of de- fects in crystals, Soviet Physics Uspekhi 13, 670 (1971)

    work page 1971

  4. [4]

    J.-R. Li, J. Lee, W. Huang, S. Burchesky, B. Shteynas, F. C ¸ . Top, A. O. Jamison, and W. Ketterle, A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates, Nature 543, 91 (2017)

    2017

  5. [5]

    Tanzi, S

    L. Tanzi, S. M. Roccuzzo, E. Lucioni, F. Fam` a, A. Fioretti, C. Gabbanini, G. Modugno, A. Recati, and S. Stringari, Supersolid symmetry breaking from com- pressional oscillations in a dipolar quantum gas, Nature 574, 382 (2019)

    2019

  6. [6]

    323, approximately half of ln 2—the full saturation en- tropy of a spin- 1 2 system. In our model, quantum fluctuations arising from first- order corrections in Jxy are expected to lift the extensive ground-state degeneracy by selecting a specific ground- state submanifold within the Wannier subspace. Conse- quently, the Wannier entropy should be recovered a...

  7. [7]

    In the pure Ising model, dispersionless single- magnon bands are predicted at energies E = nJzz with n = 1, 2, 3, corresponding to spin-flip excitations within a locally magnetized environment as illustrated in Fig- ure

  8. [8]

    It becomes slightly dispersive due to the nonzero Jxy (α ≈ 0

    The observed high-energy excitation corresponds to the spin flip excitation with n = 1. It becomes slightly dispersive due to the nonzero Jxy (α ≈ 0. 08 in K2Co(SeO3)2), with the bottom of the branch located at the K point. The average energy of the excitation is con- sistent with the exchange interaction Jzz = 3. 1 meV, as deduced from high-field magnetiza...

Show all 86 references
  1. [9]

    5-9 have been averaged over equivalent paths in the reciprocal space accessible in the experiment, as shown in Supplementary Figure 3 and Supplementary Figure 5

    Note that to enhance the count- ing statistics of the neutron intensity, the INS data pre- sented in Fig. 5-9 have been averaged over equivalent paths in the reciprocal space accessible in the experiment, as shown in Supplementary Figure 3 and Supplementary Figure 5. To better...

  2. [10]

    16 K < T <3. 27 K. The comparison with the experi- ment is presented in Figure

  3. [11]

    superfluidity

    The energy resolution of this dataset (∆ E ≈ 40 µ eV) is lower than that obtained at AMATERAS [Figure 5 and Figure 6]. While the low- energy spectrum at zero magnetic field [Figure 10(a) and Figure 11(a),(e)] appears qualitatively similar in both measurements, the application o...

  4. [12]

    pseudo-Goldstone

    Al- though we cannot entirely rule out the possibility of an- tiferromagnetic interlayer correlations characterized by a coupling constantJ§, the absence of a jump or noticeable change in the slope of the magnetization curve suggests that each individual layer has zero net mag...

  5. [13]

    25, and 0 . 5 T. The white dots indicate the lowest en- ergy pole (first pole) of the DSSF extracted from the QMC data as presented in Methods. Since the QMC simulations are performed in imaginary time, an analytic continuation is applied to transform the dynamical cor- relatio...

  6. [14]

    Differential Evolution Algorithm

    5 T [Figure 18(c)]. Figure 11(e-g) compares the QMC calculations with experimental data at the M-point, demonstrating that our simulations accurately predict the location of the lowest-energy quasiparticle peak. This agreement is fur- ther supported by the good match between t...

  7. [15]

    To address the sign problem, the original XXZ Hamiltonian is projected onto the Wannier space where the transformation introduced by Wang per- mits reverse the sign of the xy-term without altering the 12 thermodynamic properties or the ïSz i (t)Sz j (0)ð correla- tion function...

  8. [16]

    The phonon and Schottky contributions were subtracted from the measured data as in Figure 3(b). The mentioned low-temperature broad peaks are successfully reproduced by the QMC simula- tions of the low-energy effective model, confirming the validity of the Hamiltonian parameters...

  9. [17]

    Boninsegni and N

    M. Boninsegni and N. V. Prokof’ev, Colloquium: Super- solids: What and where are they?, Rev. Mod. Phys. 84, 759 (2012)

    2012

  10. [18]

    M. Guo, F. B¨ ottcher, J. Hertkorn, J.-N. Schmidt, M. Wenzel, H. P. B¨ uchler, T. Langen, and T. Pfau, The low-energy Goldstone mode in a trapped dipolar super- solid, Nature 574, 386 (2019)

    2019

  11. [19]

    Heidarian and K

    D. Heidarian and K. Damle, Persistent supersolid phase of hard-core bosons on the triangular lattice, Phys. Rev. Lett. 95, 127206 (2005)

    2005

  12. [20]

    Wessel and M

    S. Wessel and M. Troyer, Supersolid hard-core bosons on the triangular lattice, Phys. Rev. Lett. 95, 127205 (2005)

    2005

  13. [21]

    R. G. Melko, A. Paramekanti, A. A. Burkov, A. Vish- wanath, D. N. Sheng, and L. Balents, Supersolid order from disorder: Hard-core bosons on the triangular lattice, Phys. Rev. Lett. 95, 127207 (2005)

    2005

  14. [22]

    Momoi and K

    T. Momoi and K. Totsuka, Magnetization plateaus of the Shastry-Sutherland model for SrCu 2(BO3)2: Spin- density wave, supersolid, and bound states, Phys. Rev. B 62, 15067 (2000)

    2000

  15. [23]

    Sengupta and C

    P. Sengupta and C. D. Batista, Spin supersolid in an anisotropic spin-one Heisenberg chain, Phys. Rev. Lett. 99, 217205 (2007) . 17

    2007

  16. [24]

    Heydarinasab and J

    F. Heydarinasab and J. Abouie, Spin supersolid phase in coupled alternating spin chains, Scientific Reports 8, 7955 (2018)

    2018

  17. [25]

    Gao, Y.-C

    Y. Gao, Y.-C. Fan, H. Li, F. Yang, X.-T. Zeng, X.-L. Sheng, R. Zhong, Y. Qi, Y. Wan, and W. Li, Spin su- persolidity in nearly ideal easy-axis triangular quantum antiferromagnet Na 2BaCo(PO4)2, npj Quantum Materi- als 7, 89 (2022)

    2022

  18. [26]

    J. Wang, H. Li, N. Xi, Y. Gao, Q.-B. Yan, W. Li, and G. Su, Plaquette singlet transition, magnetic barocaloric effect, and spin supersolidity in the Shastry-Sutherland model, Phys. Rev. Lett. 131, 116702 (2023)

    2023

  19. [27]

    Miyashita, Magnetic properties of Ising-like Heisen- berg antiferromagnets on the triangular lattice, Journal of the Physical Society of Japan 55, 3605 (1986)

    S. Miyashita, Magnetic properties of Ising-like Heisen- berg antiferromagnets on the triangular lattice, Journal of the Physical Society of Japan 55, 3605 (1986)

    1986

  20. [28]

    Yamamoto, G

    D. Yamamoto, G. Marmorini, and I. Danshita, Quantum phase diagram of the triangular-lattice XXZ model in a magnetic field, Phys. Rev. Lett. 112, 127203 (2014)

    2014

  21. [29]

    Sellmann, X.-F

    D. Sellmann, X.-F. Zhang, and S. Eggert, Phase diagram of the antiferromagnetic XXZ model on the triangular lattice, Phys. Rev. B 91, 081104 (2015)

    2015

  22. [30]

    M. M. Bordelon, E. Kenney, C. Liu, T. Hogan, L. Posthuma, M. Kavand, Y. Lyu, M. Sherwin, N. P. Butch, C. Brown, M. J. Graf, L. Balents, and S. D. Wil- son, Field-tunable quantum disordered ground state in the triangular-lattice antiferromagnet NaYbO 2, Nature Physics 15, 1058 (2019)

    2019

  23. [31]

    J. Wu, J. Li, Z. Zhang, C. Liu, Y. H. Gao, E. Feng, G. Deng, Q. Ren, Z. Wang, R. Chen, J. Embs, F. Zhu, Q. Huang, Z. Xiang, L. Chen, Y. Wu, E. S. Choi, Z. Qu, L. Li, J. Wang, H. Zhou, Y. Su, X. Wang, G. Chen, Q. Zhang, and J. Ma, Magnetic field effects on the quan- tum spin liqu...

    2022

  24. [32]

    J. Ma, Y. Kamiya, T. Hong, H. B. Cao, G. Ehlers, W. Tian, C. D. Batista, Z. L. Dun, H. D. Zhou, and M. Matsuda, Static and dynamical properties of the spin-1 / 2 equilateral triangular-lattice antiferromag- net Ba 3CoSb2O9, Phys. Rev. Lett. 116, 087201 (2016)

    2016

  25. [33]

    K. P. Schmidt, J. Dorier, A. M. L¨ auchli, and F. Mila, Supersolid phase induced by correlated hopping in spin- 1/ 2 frustrated quantum magnets, Phys. Rev. Lett. 100, 090401 (2008)

    2008

  26. [34]

    G. H. Wannier, Antiferromagnetism. the triangular Ising net, Phys. Rev. 79, 357 (1950)

    1950

  27. [35]

    Matsubara and H

    T. Matsubara and H. Matsuda, A Lattice Model of Liquid Helium, I, Progress of Theoretical Physics 16, 569 (1956)

    1956

  28. [37]

    Heidarian and A

    D. Heidarian and A. Paramekanti, Supersolidity in the triangular lattice spin-1/ 2 XXZ model: A variational per- spective, Phys. Rev. Lett. 104, 015301 (2010)

    2010

  29. [38]

    C. A. Gallegos, S. Jiang, S. R. White, and A. L. Cherny- shev, Phase diagram of the easy-axis triangular-lattice J1− J2 model, Phys. Rev. Lett. 134, 196702 (2025)

    2025

  30. [39]

    Alicea, A

    J. Alicea, A. V. Chubukov, and O. A. Starykh, Quan- tum stabilization of the 1 / 3-magnetization plateau in Cs2CuBr4, Phys. Rev. Lett. 102, 137201 (2009)

    2009

  31. [40]

    Kamiya, L

    Y. Kamiya, L. Ge, T. Hong, Y. Qiu, D. L. Quintero- Castro, Z. Lu, H. B. Cao, M. Matsuda, E. S. Choi, C. D. Batista, M. Mourigal, H. D. Zhou, and J. Ma, The nature of spin excitations in the one-third magnetization plateau phase of Ba 3CoSb2O9, Nature Communications 9, 2666 (2018)

    2018

  32. [41]

    F. Wang, F. Pollmann, and A. Vishwanath, Extended supersolid phase of frustrated hard-core bosons on a tri- angular lattice, Phys. Rev. Lett. 102, 017203 (2009)

    2009

  33. [42]

    H. C. Jiang, M. Q. Weng, Z. Y. Weng, D. N. Sheng, and L. Balents, Supersolid order of frustrated hard-core bosons in a triangular lattice system, Phys. Rev. B 79, 020409 (2009)

    2009

  34. [43]

    Y. Xu, J. Hasik, B. Ponsioen, and A. H. Nevidomskyy, Simulating spin dynamics of supersolid states in a quan- tum ising magnet, Phys. Rev. B 111, L060402 (2025)

    2025

  35. [44]

    Murthy, D

    G. Murthy, D. Arovas, and A. Auerbach, Superfluids and supersolids on frustrated two-dimensional lattices, Phys. Rev. B 55, 3104 (1997)

    1997

  36. [45]

    M. Zhu, V. Romerio, N. Steiger, S. D. Nabi, N. Mu- rai, S. Ohira-Kawamura, K. Y. Povarov, Y. Skourski, R. Sibille, L. Keller, Z. Yan, S. Gvasaliya, and A. Zhe- ludev, Continuum excitations in a spin supersolid on a triangular lattice, Phys. Rev. Lett. 133, 186704 (2024)

    2024

  37. [46]

    T. Chen, A. Ghasemi, J. Zhang, L. Shi, Z. Tagay, L. Chen, E.-S. Choi, M. Jaime, M. Lee, Y. Hao, H. Cao, B. Winn, R. Zhong, X. Xu, N. P. Armitage, R. Cava, and C. Broholm, Phase diagram and spectroscopic evidence of supersolids in quantum ising magnet K 2Co(SeO3)2 (2024), arXiv...

    2024

  38. [47]

    Zhong, S

    R. Zhong, S. Guo, and R. J. Cava, Frustrated magnetism in the layered triangular lattice materials K 2Co(SeO3)2 and Rb 2Co(SeO3)2, Phys. Rev. Mater. 4, 084406 (2020)

    2020

  39. [48]

    Anderson, Resonating valence bonds: A new kind of insulator?, Materials Research Bulletin 8, 153 (1973)

    P. Anderson, Resonating valence bonds: A new kind of insulator?, Materials Research Bulletin 8, 153 (1973)

    1973

  40. [49]

    Balents, Spin liquids in frustrated magnets, Nature 464, 199 EP (2010)

    L. Balents, Spin liquids in frustrated magnets, Nature 464, 199 EP (2010)

    2010

  41. [50]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a re- view, Reports on Progress in Physics 80, 016502 (2016)

    2016

  42. [51]

    Broholm, R

    C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science 367, eaay0668 (2020)

    2020

  43. [52]

    E. A. Ghioldi, S.-S. Zhang, Y. Kamiya, L. O. Manuel, A. E. Trumper, and C. D. Batista, Evidence of two- spinon bound states in the magnetic spectrum of Ba3CoSb2O9, Phys. Rev. B 106, 064418 (2022)

    2022

  44. [53]

    Sengupta, A

    P. Sengupta, A. W. Sandvik, and R. R. P. Singh, Specific heat of quasi-two-dimensional antiferromagnetic heisen- berg models with varying interplanar couplings, Phys. Rev. B 68, 094423 (2003)

    2003

  45. [55]

    M. B. Stone, D. H. Reich, C. Broholm, K. Lefmann, C. Rischel, C. P. Landee, and M. M. Turnbull, Extended Quantum Critical Phase in a Magnetized Spin-1 / 2 Anti- ferromagnetic Chain, Phys. Rev. Lett. 91, 037205 (2003)

    2003

  46. [56]

    Kleine, E

    B. Kleine, E. M¨ uller-Hartmann, K. Frahm, and P. Fazekas, Spin-wave analysis of easy-axis quantum an- tiferromagnets on the triangular lattice, Zeitschrift f¨ ur Physik B Condensed Matter 87, 103 (1992)

    1992

  47. [57]

    Sheng and C

    Q. Sheng and C. L. Henley, Ordering due to disorder in a triangular heisenberg antiferromagnet with exchange anisotropy, Journal of Physics: Condensed Matter 4, 2937 (1992) . 18

    1992

  48. [58]

    Kawamura and S

    H. Kawamura and S. Miyashita, Phase transition of the heisenberg antiferromagnet on the triangular lattice in a magnetic field, Journal of the Physical Society of Japan 54, 4530 (1985)

    1985

  49. [59]

    Savary, K

    L. Savary, K. A. Ross, B. D. Gaulin, J. P. C. Ruff, and L. Balents, Order by quantum disorder in Er 2Ti2O7, Phys. Rev. Lett. 109, 167201 (2012)

    2012

  50. [60]

    J. G. Rau, P. A. McClarty, and R. Moessner, Pseudo- Goldstone gaps and order-by-quantum disorder in frus- trated magnets, Phys. Rev. Lett. 121, 237201 (2018)

    2018

  51. [61]

    J. V. Jos´ e, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nel- son, Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model, Phys. Rev. B 16, 1217 (1977)

    1977

  52. [62]

    Stephan and B

    W. Stephan and B. W. Southern, Monte carlo study of the anisotropic heisenberg antiferromagnet on the trian- gular lattice, Phys. Rev. B 61, 11514 (2000)

    2000

  53. [63]

    Melchy and M

    P.-E. Melchy and M. E. Zhitomirsky, Interplay of anisotropy and frustration: Triple transitions in a triangular-lattice antiferromagnet, Phys. Rev. B 80, 064411 (2009)

    2009

  54. [64]

    A. Sen, P. Dutt, K. Damle, and R. Moessner, Variational wave-function study of the triangular lattice supersolid, Physical Review Letters 100, 147204 (2008)

    2008

  55. [65]

    Ulaga, J

    M. Ulaga, J. Kokalj, A. Wietek, A. Zorko, and P. Prelovˇ sek, Finite-temperature properties of the easy- axis Heisenberg model on frustrated lattices, Phys. Rev. B 109, 035110 (2024)

    2024

  56. [66]

    Ulaga, J

    M. Ulaga, J. Kokalj, T. Tohyama, and P. Prelovˇ sek, Easy- axis heisenberg model on the triangular lattice: From a supersolid to a gapped solid, Phys. Rev. B 111, 174442 (2025)

    2025

  57. [67]

    A. L. Chernyshev and M. E. Zhitomirsky, Spin waves in a triangular lattice antiferromagnet: Decays, spec- trum renormalization, and singularities, Phys. Rev. B 79, 144416 (2009)

    2009

  58. [68]

    E. A. Ghioldi, M. G. Gonzalez, S.-S. Zhang, Y. Kamiya, L. O. Manuel, A. E. Trumper, and C. D. Batista, Dy- namical structure factor of the triangular antiferromag- net: Schwinger boson theory beyond mean field, Phys. Rev. B 98, 184403 (2018)

    2018

  59. [69]

    A. Bose, K. Hart, R. Sutcliffe, and A. Paramekanti, Mod- ified large- n approach to gapless spin liquids, magnetic orders, and dynamics: Application to triangular lattice antiferromagnets, Phys. Rev. B 111, 214410 (2025)

    2025

  60. [70]

    H. Jia, B. Ma, Z. D. Wang, and G. Chen, Quantum spin supersolid as a precursory Dirac spin liquid in a trian- gular lattice antiferromagnet, Phys. Rev. Res. 6, 033031 (2024)

    2024

  61. [71]

    Y. Gao, C. Zhang, J. Xiang, D. Yu, X. Lu, P. Sun, W. Jin, G. Su, and W. Li, Double magnon-roton excitations in the triangular-lattice spin supersolid, Phys. Rev. B 110, 214408 (2024)

    2024

  62. [72]

    R. Chi, J. Hu, H.-J. Liao, and T. Xiang, Dynamical spec- tra of spin supersolid states in triangular antiferromag- nets, Phys. Rev. B 110, L180404 (2024)

    2024

  63. [73]

    Xiang, C

    J. Xiang, C. Zhang, Y. Gao, W. Schmidt, K. Schmalzl, C.-W. Wang, B. Li, N. Xi, X.-Y. Liu, H. Jin, G. Li, J. Shen, Z. Chen, Y. Qi, Y. Wan, W. Jin, W. Li, P. Sun, and G. Su, Giant magnetocaloric effect in spin supersolid candidate Na 2BaCo(PO4)2, Nature 625, 270 (2024)

    2024

  64. [74]

    Sheng, L

    J. Sheng, L. Wang, W. Jiang, H. Ge, N. Zhao, T. Li, M. Kofu, D. Yu, W. Zhu, J.-W. Mei, Z. Wang, and L. Wu, Continuum of spin excitations in an ordered magnet, The Innovation 6, 100769 (2025)

    2025

  65. [75]

    Sheng, L

    J. Sheng, L. Wang, A. Candini, and L. Wu, Two- dimensional quantum universality in the spin- 1/2 triangular-lattice quantum antiferromagnet Na2BaCo(PO4)2, PNAS 119, e2211193119 (2022)

    2022

  66. [76]

    M. Shu, W. Dong, J. Jiao, J. Wu, G. Lin, Y. Kamiya, T. Hong, H. Cao, M. Matsuda, W. Tian, S. Chi, G. Ehlers, Z. Ouyang, H. Chen, Y. Zou, Z. Qu, Q. Huang, H. Zhou, and J. Ma, Static and dynamical properties of the spin- 5 2 nearly ideal triangular lattice antiferromagnet Ba3MnS...

    2023

  67. [77]

    Powalski, G

    M. Powalski, G. S. Uhrig, and K. P. Schmidt, Roton min- imum as a fingerprint of magnon-Higgs scattering in or- dered quantum antiferromagnets, Phys. Rev. Lett. 115, 207202 (2015)

    2015

  68. [78]

    Wildner, Isotypism of a selenite with a car- bonate: structure of the buetschliite-type compound K2Co(SeO3)2, Acta Crystallographica Section C 48, 410 (1992)

    M. Wildner, Isotypism of a selenite with a car- bonate: structure of the buetschliite-type compound K2Co(SeO3)2, Acta Crystallographica Section C 48, 410 (1992)

    1992

  69. [79]

    Nakajima, S

    K. Nakajima, S. Ohira-Kawamura, T. Kikuchi, M. Naka- mura, R. Kajimoto, Y. Inamura, N. Takahashi, K. Aizawa, K. Suzuya, K. Shibata, T. Nakatani, K. Soyama, R. Maruyama, H. Tanaka, W. Kambara, T. Iwahashi, Y. Itoh, T. Osakabe, S. Wakimoto, K. Kaku- rai, F. Maekawa, M. Harada, K...

    2011

  70. [80]

    Ewings, A

    R. Ewings, A. Buts, M. Le, J. van Duijn, I. Bustin- duy, and T. Perring, Horace: Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments, Nuclear Instruments and Methods in Physics Research Section A: Acceler- ators, ...

    2016

  71. [81]

    Dahlbom, H

    D. Dahlbom, H. Zhang, C. Miles, S. Quinn, A. Niraula, B. Thipe, M. Wilson, S. Matin, H. Mankad, S. Hahn, et al., Sunny. jl: A julia package for spin dynamics, arXiv preprint arXiv:2501.13095 (2025)

    2025 arXiv

  72. [82]

    Kato and N

    Y. Kato and N. Kawashima, Quantum Monte Carlo method for the Bose-Hubbard model with harmonic con- fining potential, Phys. Rev. E 79, 021104 (2009)

    2009

  73. [83]

    Motoyama, K

    Y. Motoyama, K. Yoshimi, A. Masaki-Kato, T. Kato, and N. Kawashima, DSQSS: Discrete Space Quantum Systems Solver, Comput. Phys. Commun. 264, 107944 (2021)

    2021

  74. [84]

    Zhang, K

    Z. Zhang, K. Wierschem, I. Yap, Y. Kato, C. D. Batista, and P. Sengupta, Phase diagram and magnetic excita- tions of anisotropic spin-one magnets, Phys. Rev. B 87, 174405 (2013)

    2013

  75. [85]

    N. S. Nichols, P. Sokol, and A. Del Maestro, Parameter- free differential evolution algorithm for the analytic con- tinuation of imaginary time correlation functions, Phys. Rev. E 106, 025312 (2022)

    2022

  76. [86]

    Wannier states and spin supersolid physics i n the triangular antiferromagnet K 2Co(SeO3)2

    J. Neuhaus, N. S. Nichols, D. Banerjee, B. Cohen-Stead, T. A. Maier, A. D. Maestro, and S. Johnston, Smo- qydeac.jl: A differential evolution package for the ana- lytic continuation of imaginary time correlation functions (2024), arXiv:2407.04568 [cond-mat.stat-mech] . Suppleme...

    2024 arXiv

  77. [87]

    Y. Fu, H. Ge, J. Chen, J. Xiao, Y. Tan, L. Wang, J. Wang, C. Don g, Z. Qu, M. He, C. Xi, L. Ling, B. Xi, and J.-W. Mei, Berezinskii-kosterlitz-thouless region and magnetizat ion plateaus in easy-axis triangular weak-dimer antiferromagn et K2Co2(SeO3)3, arXiv:2501.09619 (2025)

    2025 arXiv

  78. [88]

    M. Zhu, V. Romerio, N. Steiger, S. D. Nabi, N. Murai, S. Ohira-Ka wamura, K. Y. Povarov, Y. Skourski, R. Sibille, L. Keller, Z. Yan, S. Gvasaliya, and A. Zheludev, Continuum excitation s in a spin supersolid on a triangular lattice, Phys. Rev. Lett. 133, 186704 (2024)

    2024

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