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REVIEW 4 major objections 5 minor 49 references

Close to field-driven dimensional reduction, a quasi-2D quantum magnet shows the golden-ratio massive spectrum of emergent E8 symmetry.

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2026-07-30 19:24 UTC pith:ZCM4BLBM

load-bearing objection Real multi-probe data in a new host for E8-like physics, but the golden-ratio field is chosen by hand and the Ising deformation is imported, not derived. the 4 major comments →

arxiv 2607.23547 v1 pith:ZCM4BLBM submitted 2026-07-26 cond-mat.str-el quant-ph

Observation of an emergent energy scale close to dimensional reduction in a quasi-two-dimensional quantum magnet

Anneke Reinold , Laur Peedu , Kirill Amelin , Urmas Nagel , Toomas R\~{o}\~{o}m , Sven Luther , Hannes K\"uhne , Dirk Wulferding
show 14 more authors
Kingshuk Mukhuti Maarten W. de Dreu Peter C. M. Christianen Dennis Kudlacik Dmitri Yakovlev Zhiying Zhao Taro Nakajima Yoshimitsu Kohama Thomas Lorenz Franco Lisandrini Corinna Kollath Marcin Raczkowski Fakher F. Assaad Zhe Wang
This is my paper
classification cond-mat.str-el quant-ph
keywords E8 symmetrytransverse-field Ising chaindimensional reductionquantum magnetCu2(OH)3BrTHz spectroscopyemergent massive spectrumbound states
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.

This paper reports that in the quasi-two-dimensional magnet Cu2(OH)3Br, a transverse magnetic field nearly polarizes the ferromagnetic copper chains and decouples them from the antiferromagnetic ones, suppressing three-dimensional order. Just below that dimensional-reduction transition, terahertz spectroscopy resolves a set of massive spin excitations whose two lowest energies stand in the golden ratio 1.618, with higher peaks lining up with the single- and two-particle levels fixed by the integrable E8 Toda field theory of a perturbed transverse-field Ising chain. The authors read this as spectroscopic evidence that an emergent E8 symmetry and its bound-state spectrum appear in the ferromagnetic sublattice, slightly off criticality. A sympathetic reader cares because solid-state hosts of such integrable emergent symmetries have been rare, and the work shows that dimensional reduction in a mixed-chain magnet can recreate the same characteristic dynamics previously associated only with quasi-one-dimensional Ising compounds.

Core claim

Near the transverse-field-induced dimensional reduction in Cu2(OH)3Br, the ferromagnetic Cu1 sublattice hosts a characteristic massive spectrum: the ratio m2/m1 reaches the golden ratio 1.618 at 9.8 T, and higher features match the E8 single- and multiparticle scale (m3, m1+m1, m4, and possibly m1+m2), providing evidence for emergent E8 symmetry and its bound-state excitations.

What carries the argument

The emergent E8 massive spectrum of the integrable affine Toda field theory that describes a critical transverse-field Ising chain weakly deformed by a longitudinal field; it fixes the mass ratios (starting with the golden ratio) and the multiparticle channels matched to the THz data.

Load-bearing premise

That the ferromagnetic copper chains act as a transverse-field Ising model weakly tilted by a longitudinal field from residual interchain order, even though the microscopic spin model that fits the magnetization has continuous spin symmetry and cannot itself produce the observed spectrum.

What would settle it

A higher-resolution THz or inelastic-neutron map at 9.8 T showing that the higher peaks do not sit at the E8 positions (m3 ≈ 1.989 m1, m4 ≈ 2.405 m1, m1+m1 continuum edge), or a polarization/form-factor test proving those modes belong to the antiferromagnetic Cu2 chains rather than the ferromagnetic Cu1 sublattice.

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

If this is right

  • Integrable E8 field theory can describe emergent dynamics near dimensional-reduction transitions, not only near one-dimensional Ising critical points.
  • Quasi-two-dimensional magnets built from alternating ferro- and antiferromagnetic chains become candidate hosts for emergent Lie-algebra spectra.
  • The golden-ratio mass ratio and multiparticle continuum edges serve as spectroscopic fingerprints for identifying perturbed Ising criticality in other materials.
  • Dimensional reduction can be used as an experimental tuning knob to approach the regime where an infinite set of integrals of motion emerges.

Where Pith is reading between the lines

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

  • Similar E8 fingerprints may appear in other mixed-chain cuprates whenever field polarization of one sublattice isolates Ising-like chains that still feel a weak longitudinal coupling from residual order.
  • If the Ising anisotropy is only moderate, the observed mass ratios should drift with field away from pure E8 values, giving a direct spectroscopic measure of the longitudinal deformation strength.
  • Mapping the same THz window above the second sublattice’s saturation field would test whether the E8 scale collapses once both chain species are fully polarized.

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

4 major / 5 minor

Summary. The manuscript reports NMR (1/T1 and spectral shift), high-field Raman, and THz absorption measurements on the quasi-2D spin-1/2 magnet Cu2(OH)3Br in fields B∥b up to 17–23 T. Three probes consistently map the boundary T_N(B) between 3D order and a field-induced disordered phase associated with polarization of the ferromagnetic Cu1 chains and effective Cu1–Cu2 decoupling ("dimensional reduction"), in agreement with prior Cp/M data and QMC. In the ordered phase at 9–10 T, the THz spectra show several modes; the ratio m2/m1 of the two lowest crosses the golden ratio at B = 9.8 T, and at that field the higher peaks are overlaid on the E8 single- and two-particle ladder (m3, m1+m1, m4, possibly m1+m2) scaled by m1. The authors interpret this as evidence for emergent E8 symmetry of a longitudinally perturbed transverse-field Ising chain realized on the Cu1 sublattice, while acknowledging that the SU(2)-symmetric microscopic model that fits the magnetization "cannot account for the present experimental data."

Significance. If the E8 identification holds, this would be a notable extension of emergent-integrability physics beyond CoNb2O6 and BaCo2V2O8 to a new setting — ferromagnetic chains near a field-driven dimensional-reduction transition in a quasi-2D system — and would support the generality of Zamolodchikov's E8 spectrum as a description of perturbed Ising criticality. The experimental effort is substantial and a genuine strength: three independent spectroscopies plus thermodynamics agree on a single phase boundary, the high-field Raman and THz datasets are of good quality, and the comparison to the integrable theory is in principle falsifiable through fixed mass ratios. The authors are also commendably explicit that the SU(2) model fitting the thermodynamics fails the spectroscopy. However, the evidentiary weight of the E8 claim is currently overstated: the golden-ratio point is selected rather than predicted, and the independent content of the ladder comparison is thinner than the presentation suggests (see major comments).

major comments (4)
  1. [Fig. 4(c)-(d) and associated text] The field B* = 9.8 T is defined as the point where the measured m2/m1 equals 1.618 (Fig. 4c, dashed line), and the same spectrum is then compared to the E8 ladder scaled by m1 (Fig. 4d). Since m1 hardens and m2 softens monotonically with field, m2/m1 necessarily sweeps through 1.618 at some field; the golden-ratio crossing by itself therefore carries no information. In Fig. 4(d), m1 and m2 match by construction, and m3 (1.989 m1) is degenerate with the m1+m1 onset (2 m1) within any realistic resolution — a two-particle onset at 2m1 is expected in any gapped system, E8 or not. The independent content of the comparison thus reduces essentially to m4 (2.405 m1) and the 'possible' m1+m2 (2.618 m1). The authors should (i) provide a table of extracted peak positions, linewidths, and uncertainties; (ii) state explicitly which dashed-line matches are independent of the fitting/selection procedur
  2. [Fig. 4(c); discussion of E8 scaling regime] In the E8 regime the mass ratios are universal constants fixed by integrability. The observed m2/m1 instead drifts monotonically from ~1.8 to ~1.5 across 9-11 T, i.e. the ratios are strongly field-dependent, which is itself evidence that the system is not in the E8 scaling regime over that window — at best it passes through a single point. Moreover, the E8 Toda theory is an asymptotic expansion about the Ising critical point, yet B* = 9.8 T lies ~25% below Bc = 13 T. The manuscript should justify quantitatively why the scaling regime extends that far from criticality (e.g. via the microscopic couplings of Ref. [44]), or reframe the result as a crossover through E8-like ratios rather than an emergent E8 phase.
  3. [Discussion paragraphs following Fig. 4] The microscopic basis for the central interpretation is asserted rather than demonstrated. The SU(2)-symmetric model that reproduces M(B) (Fig. 1a) and the zero-field INS [44] is stated to be unable to account for the data; the required Ising anisotropy is imported from linear spin-wave fits of Ref. [44], and the longitudinal field from interchain order is argued only qualitatively. For a claim of emergent E8 this gap is load-bearing: the authors should at minimum estimate the effective Ising anisotropy on the Cu1 chains and the magnitude of the interchain mean (longitudinal) field relative to the observed gaps, and explain why a model that fits the thermodynamics fails the spectroscopy.
  4. [Fig. 4(a)-(b); mode assignment] The assignment of the THz peaks to single-particle E8 modes of the ferromagnetic Cu1 chains — as opposed to magnons of the ordered antiferromagnetic Cu2 sublattice, a two-magnon continuum, or other structure — is not substantiated. Only one polarization (h_omega || a) is shown; polarization-selection-rule data, a comparison of relative intensities/linewidths with the form-factor spectral weights of Refs. [21, 36], and an explicit argument for the Cu1 (rather than Cu2) origin of m1 and m2 would substantially strengthen the identification. The tentative broad feature above Bc (circles in Fig. 4b) is said to 'hardly exceed experimental uncertainties' — this should be quantified.
minor comments (5)
  1. [Figs. 1, 3, 4] The critical field is quoted as Bc ≃ 16.3 T (QMC, Fig. 1a), 14 T (Raman section), and 13 T (THz at 3 K). While partly a temperature dependence of T_N(B), the remaining discrepancy between the QMC value and experiment should be discussed explicitly, and each Bc value should be tagged with its temperature and method.
  2. [NMR section, paragraph after Fig. 2] The text refers to 'the phase diagram in Fig. 1(c)', but the phase diagram is Fig. 1(b); Fig. 1 has only panels (a) and (b).
  3. [Fig. 4] Axis label reads 'Magnetic field B (Telsa)' — typo. In Fig. 4(b) the dual units (cm^-1 for Delta-alpha/omega vs meV photon energy) would benefit from a clearer conversion note, and the reference used to define the field-induced change Delta-alpha should be stated.
  4. [Raman section / Fig. 3] The zero-field broad continuum above ~4 meV is assigned to spinons of the AF Cu2 chains following Ref. [44]; a brief statement of why the sharp modes below Bc are instead attributed to the ordered (Cu1/Cu2) magnons, and how this squares with the later Cu1-only assignment of the THz modes, would help the reader.
  5. [General] The phrase 'in good agreement with the E8 excitations m1, m2, m3, m1+m1, m4 and possibly also m1+m2' conflates single-particle states with continuum onsets; please distinguish sharp resonances from continuum thresholds in both the figure and text. It would also help to state the field step and frequency resolution of the THz scans used to extract m2/m1 in Fig. 4(c), and to show error bars on that ratio.

Circularity Check

1 steps flagged

Field for E8 comparison is chosen where measured m2/m1 equals the golden ratio; m1/m2 match is then by construction, while higher multiparticle peaks remain an independent test.

specific steps
  1. fitted input called prediction [Fig. 4(c–d) and surrounding text (pp. 4–5)]
    "m2/m1 reaches the golden ratio of 1.618 at 9.8 T, marked by the dashed line. (d) Δα/ω spectrum at 9.8 T in comparison to the energy scale (top scale) of emergent quasiparticles governed by the E8 symmetry. ... the energy scale of the observed excitations is in good agreement with the E8 excitations m1, m2, m3, m1+m1, m4 and possibly also m1+m2."

    B=9.8 T is selected precisely so that the experimental ratio m2/m1 equals the E8 golden ratio; the overall energy unit is then fixed by the measured m1. Under that choice the placements of m1 and m2 on the E8 ladder are true by construction. Only the subsequent alignment of higher peaks (m3, 2m1, m4, …) constitutes an independent check. Presenting the golden-ratio match itself as primary observational evidence therefore overstates what is freely predicted.

full rationale

The paper’s central spectroscopic claim is that near dimensional reduction the Cu1-chain spectrum matches the E8 massive tower. The load-bearing comparison is performed at the single field B=9.8 T that is defined, in Fig. 4(c), as the point where the measured ratio m2/m1 equals the E8 value 1.618; the same spectrum is then overlaid on the E8 ladder scaled by the measured m1 (Fig. 4d). Consequently the m1 and m2 assignments cannot fail once that field and overall scale are chosen. Independent content remains: whether additional resolved peaks sit at the predicted m3≈1.989 m1, 2m1, m4≈2.405 m1, etc., and whether the ratio ever crosses φ inside the ordered phase at all. E8 mass ratios themselves are external (Zamolodchikov and subsequent integrable-field-theory literature), and self-citations to the authors’ prior magnetization and neutron work supply materials context rather than a uniqueness theorem that forces the spectrum. The result is therefore only partially circular—standard field-selection practice in the E8-magnet literature—not a derivation that reduces wholly to its inputs. Score 4 reflects one clear fitted-input step that weakens the golden-ratio ‘observation’ while leaving the multi-peak test non-vacuous.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The load-bearing jump is from multi-probe spectra near dimensional reduction to 'emergent E8 in FM Cu1 chains.' That jump imports Zamolodchikov E8 Toda mass ratios, treats interchain order as a longitudinal TFIM deformation, and relies on Ising anisotropy not present in the SU(2) Hamiltonian used for M(B). The only sharp experimental handle is mass ratios at a field chosen so m2/m1=φ.

free parameters (3)
  • Field B* where E8 comparison is made = 9.8 T
    Chosen as the field where measured m2/m1 equals the golden ratio (reported 9.8 T), then used to scale and assign the full ladder.
  • Overall E8 energy unit (m1 frequency at B*) = m1 at 9.8 T (from THz spectrum)
    Sets the absolute scale of the dashed E8 markers in Fig. 4d; only ratios are predicted by theory.
  • Effective Ising anisotropy on FM Cu1 chains = qualitative / from prior LSWT
    Required for a TFIM description; taken as suggested by prior linear spin-wave fits to neutrons, not refit or derived in this work.
axioms (5)
  • domain assumption Mass ratios of the E8 affine Toda field theory (m2/m1=φ, m3/m1≈1.989, m4/m1≈2.405, etc.) describe the low-energy spectrum of a critical TFIM deformed by a small longitudinal field.
    Invoked throughout abstract and Fig. 4 discussion via Zamolodchikov and follow-ups; standard in the subfield but not re-derived.
  • domain assumption Above polarization of Cu1, interchain coupling is suppressed and the system undergoes dimensional reduction with loss of 3D order at Bc.
    Supported by prior QMC/magnetization on this compound and consistent NMR/Raman/THz boundaries here.
  • ad hoc to paper Interchain coupling in the ordered phase acts as a small longitudinal field on the Cu1 TFIM, generating the E8 deformation.
    Stated qualitatively in the discussion after Fig. 4 without a computed longitudinal-field strength or explicit lattice-to-field-theory map for this compound.
  • ad hoc to paper Dominant exchange anisotropy is Ising-like on the ferromagnetic chains, despite an SU(2)-symmetric model fitting M(B).
    Paper explicitly notes the SU(2) model cannot account for the THz data and points to prior spin-wave anisotropy on FM chains.
  • ad hoc to paper Observed THz peaks at B* are single-particle m1–m4 and selected two-particle channels rather than unrelated magnons or continuum structure.
    Assignment in Fig. 4d by energy coincidence; stability arguments cited from E8 correlation-function literature.

pith-pipeline@v1.2.0-grok45-kimik3 · 15918 in / 3882 out tokens · 79892 ms · 2026-07-30T19:24:19.351956+00:00 · methodology

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read the original abstract

By appropriately perturbing a critical transverse-field Ising chain away from its critical point, the system can develop a finite correlation length with a characteristic purely massive spectrum, whose ratios and correlations are precisely described by an integrable field theory and an infinite set of integrals of motion corresponding to the $E_8$ Lie algebra. In this work, we report on experimental observation of a characteristic massive spectrum close to transverse field-induced dimensional reduction in a quasi-two-dimensional quantum magnet Cu$_2$(OH)$_3$Br, providing evidence for an emergent $E_8$ symmetry and the corresponding excitations of bound states in the sublattice of its ferromagnetic chains. These results demonstrate the power of integrable field theory in describing emergent many-body quantum critical phenomena in condensed matter systems.

Figures

Figures reproduced from arXiv: 2607.23547 by Anneke Reinold, Corinna Kollath, Dennis Kudlacik, Dirk Wulferding, Dmitri Yakovlev, Fakher F. Assaad, Franco Lisandrini, Hannes K\"uhne, Kingshuk Mukhuti, Kirill Amelin, Laur Peedu, Maarten W. de Dreu, Marcin Raczkowski, Peter C. M. Christianen, Sven Luther, Taro Nakajima, Thomas Lorenz, Toomas R\~{o}\~{o}m, Urmas Nagel, Yoshimitsu Kohama, Zhe Wang, Zhiying Zhao.

Figure 1
Figure 1. Figure 1: (a) Total and sublattice magnetizations in the direction [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Raman spectra measured at 2 K in various applied [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Color-coded plot of THz absorption coe [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

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Works this paper leans on

49 extracted references · 1 linked inside Pith

  1. [1]

    Senthil, A

    T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science303, 1490 (2004)

    2004

  2. [2]

    A. W. Sandvik, Phys. Rev. Lett.98, 227202 (2007)

    2007

  3. [3]

    Jiang, M

    F.-J. Jiang, M. Nyfeler, S. Chandrasekharan, and U.-J. Wiese, Journal of Statistical Mechanics: Theory and Experiment2008, P02009 (2008)

    2008

  4. [4]

    R. G. Melko and R. K. Kaul, Phys. Rev. Lett.100, 017203 (2008)

    2008

  5. [5]

    A. W. Sandvik, Phys. Rev. Lett.104, 177201 (2010)

    2010

  6. [6]

    Singh, Physics3, 35 (2010)

    R. Singh, Physics3, 35 (2010)

    2010

  7. [7]

    Nahum, J

    A. Nahum, J. T. Chalker, P. Serna, M. Ortu ˜no, and A. M. So- moza, Phys. Rev. X5, 041048 (2015)

    2015

  8. [8]

    C. Wang, A. Nahum, M. A. Metlitski, C. Xu, and T. Senthil, Phys. Rev. X7, 031051 (2017)

    2017

  9. [9]

    Y . Liu, Z. Wang, T. Sato, M. Hohenadler, C. Wang, W. Guo, and F. F. Assaad, Nature Communications10, 2658 (2019)

    2019

  10. [10]

    Senthil, Deconfined quantum critical points: a review (2023), arXiv:2306.12638 [cond-mat.str-el]

    T. Senthil, Deconfined quantum critical points: a review (2023), arXiv:2306.12638 [cond-mat.str-el]

    Pith/arXiv arXiv 2023

  11. [11]

    Mila, Journal Club for Condensed Matter Physics (2023)

    F. Mila, Journal Club for Condensed Matter Physics (2023)

    2023

  12. [12]

    Y . Cui, R. Yu, and W. Yu, Chinese Physics Letters42, 047503 (2025)

    2025

  13. [13]

    Eguchi and S.-K

    T. Eguchi and S.-K. Yang, Physics Letters B224, 373 (1989)

    1989

  14. [14]

    Mussardo, Physics Reports218, 215 (1992)

    G. Mussardo, Physics Reports218, 215 (1992)

    1992

  15. [15]

    Mussardo,Statistical Field Theory(Oxford University Press, New York, 2010)

    G. Mussardo,Statistical Field Theory(Oxford University Press, New York, 2010)

    2010

  16. [16]

    Lencs ´es, G

    M. Lencs ´es, G. Mussardo, and G. Tak´acs, Journal of Physics A: Mathematical and Theoretical56, 383001 (2023)

    2023

  17. [17]

    Sachdev,Quantum Phase Transitions, 2nd ed

    S. Sachdev,Quantum Phase Transitions, 2nd ed. (Cambridge University Press, New York, 2011). 6

    2011

  18. [18]

    A. B. Zamolodchikov, Int. J. Mod. Phys. A4, 4235 (1989)

    1989

  19. [19]

    Delfino and G

    G. Delfino and G. Mussardo, Nucl. Phys. B455, 724 (1995)

    1995

  20. [20]

    Delfino and P

    G. Delfino and P. Simonetti, Phys. Lett. B383, 450 (1996)

    1996

  21. [21]

    X. Wang, H. Zou, K. H ´ods´agi, M. Kormos, G. Tak ´acs, and J. Wu, Phys. Rev. B103, 235117 (2021)

    2021

  22. [22]

    Nahum, P

    A. Nahum, P. Serna, J. T. Chalker, M. Ortu ˜no, and A. M. So- moza, Phys. Rev. Lett.115, 267203 (2015)

    2015

  23. [23]

    Serna and A

    P. Serna and A. Nahum, Phys. Rev. B99, 195110 (2019)

    2019

  24. [24]

    Ma, Y .-Z

    N. Ma, Y .-Z. You, and Z. Y . Meng, Phys. Rev. Lett.122, 175701 (2019)

    2019

  25. [25]

    Huang, D.-C

    R.-Z. Huang, D.-C. Lu, Y .-Z. You, Z. Y . Meng, and T. Xiang, Phys. Rev. B100, 125137 (2019)

    2019

  26. [26]

    T. Sato, Z. Wang, Y . Liu, D. Hou, M. Hohenadler, W. Guo, and F. F. Assaad, Phys. Rev. B108, L121111 (2023)

    2023

  27. [27]

    Liu, X.-T

    W.-Y . Liu, X.-T. Zhang, Z. Wang, S.-S. Gong, W.-Q. Chen, and Z.-C. Gu, Phys. Rev. Lett.133, 026502 (2024)

    2024

  28. [28]

    Mussardo, M

    G. Mussardo, M. Panero, and A. Stampiggi, Journal of Statisti- cal Mechanics: Theory and Experiment2024, 033103 (2024)

    2024

  29. [29]

    Fitos and G

    B. Fitos and G. Tak ´acs, Phys. Rev. D110, 085024 (2024)

    2024

  30. [30]

    Y . Cui, L. Liu, H. Lin, K.-H. Wu, W. Hong, X. Liu, C. Li, Z. Hu, N. Xi, S. Li, R. Yu, A. W. Sandvik, and W. Yu, Science 380, 1179 (2023)

    2023

  31. [31]

    Coldea, D

    R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Science327, 177 (2010)

    2010

  32. [32]

    J. A. Kj ¨all, F. Pollmann, and J. E. Moore, Phys. Rev. B83, 020407(R) (2011)

    2011

  33. [33]

    Amelin, J

    K. Amelin, J. Engelmayer, J. Viirok, U. Nagel, T. R ˜o om, T. Lorenz, and Z. Wang, Phys. Rev. B102, 104431 (2020)

    2020

  34. [34]

    Oshikawa, Journal Club for Condensed Matter Physics (2020)

    M. Oshikawa, Journal Club for Condensed Matter Physics (2020)

    2020

  35. [35]

    Amelin, J

    K. Amelin, J. Viirok, U. Nagel, T. R˜o˜om, J. Engelmayer, T. Dey, A. Agung Nugroho, T. Lorenz, and Z. Wang, Journal of Physics A: Mathematical and Theoretical55, 484005 (2022)

    2022

  36. [36]

    Zhang, K

    Z. Zhang, K. Amelin, X. Wang, H. Zou, J. Yang, U. Nagel, T. R ˜o om, T. Dey, A. A. Nugroho, T. Lorenz, J. Wu, and Z. Wang, Phys. Rev. B101, 220411 (2020)

    2020

  37. [37]

    H. Zou, Y . Cui, X. Wang, Z. Zhang, J. Yang, G. Xu, A. Okutani, M. Hagiwara, M. Matsuda, G. Wang, G. Mussardo, K. H´ods´agi, M. Kormos, Z. He, S. Kimura, R. Yu, W. Yu, J. Ma, and J. Wu, Phys. Rev. Lett.127, 077201 (2021)

    2021

  38. [38]

    X. Wang, K. Puzniak, K. Schmalzl, C. Balz, M. Matsuda, A. Okutani, M. Hagiwara, J. Ma, J. Wu, and B. Lake, Science Bulletin69, 2974 (2024)

    2024

  39. [39]

    Z. Wang, S. Reschke, D. H ¨uvonen, S.-H. Do, K.-Y . Choi, M. Gensch, U. Nagel, T. R˜o om, and A. Loidl, Phys. Rev. Lett. 119, 227202 (2017)

    2017

  40. [40]

    Pilch, L

    P. Pilch, L. Peedu, A. K. Bera, S. M. Yusuf, U. Nagel, T. R ˜o om, and Z. Wang, Phys. Rev. B108, L140406 (2023)

    2023

  41. [41]

    Pilch, L

    P. Pilch, L. Peedu, U. Nagel, T. R ˜o om, C. Zhu, Y . Skourski, X. Xu, R. J. Cava, and Z. Wang, Phys. Rev. B112, 014455 (2025)

    2025

  42. [42]

    Z. Y . Zhao, H. L. Che, R. Chen, J. F. Wang, X. F. Sun, and Z. Z. He, J. Phys. Condens. Matter31, 275801 (2019)

    2019

  43. [43]

    Reinold, L

    A. Reinold, L. Berger, M. Raczkowski, Z. Zhao, Y . Kohama, M. Gen, D. I. Gorbunov, Y . Skourski, S. Zherlitsyn, F. F. As- saad, T. Lorenz, and Z. Wang, Phys. Rev. B111, L100405 (2025)

    2025

  44. [44]

    Zhang, Z

    H. Zhang, Z. Zhao, D. Gautreau, M. Raczkowski, A. Saha, V . O. Garlea, H. Cao, T. Hong, H. O. Jeschke, S. D. Mahanti, T. Birol, F. F. Assaad, and X. Ke, Phys. Rev. Lett.125, 037204 (2020)

    2020

  45. [45]

    Wulferding, S

    D. Wulferding, S. S. Islam, Y . Choi, G. Ban, S. Lee, A. Paw- bake, C. Faugeras, and K.-Y . Choi, Phys. Rev. B111, 064409 (2025)

    2025

  46. [46]

    Testa, V

    L. Testa, V . ˇSurija, K. Prˇsa, P. Steffens, M. Boehm, P. Bourges, H. Berger, B. Normand, H. M. Rønnow, and I. ˇZivkovi´c, Phys. Rev. B103, L020409 (2021)

    2021

  47. [47]

    Wulferding, Y

    D. Wulferding, Y . Choi, S.-H. Do, C. H. Lee, P. Lemmens, C. Faugeras, Y . Gallais, and K.-Y . Choi, Nature Communica- tions11, 1603 (2020)

    2020

  48. [48]

    Sahasrabudhe, D

    A. Sahasrabudhe, D. A. S. Kaib, S. Reschke, R. German, T. C. Koethe, J. Buhot, D. Kamenskyi, C. Hickey, P. Becker, V . Tsurkan, A. Loidl, S. H. Do, K. Y . Choi, M. Gr¨uninger, S. M. Winter, Z. Wang, R. Valent´ı, and P. H. M. van Loosdrecht, Phys. Rev. B101, 140410 (2020)

    2020

  49. [49]

    F. F. Assaad, M. Bercx, F. Goth, A. G ¨otz, J. S. Hofmann, E. Huffman, Z. Liu, F. P. Toldin, J. S. E. Portela, and J. Schwab, SciPost Phys. Codebases , 1 (2025)

    2025