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arxiv: 2604.16820 · v1 · submitted 2026-04-18 · ❄️ cond-mat.str-el

Recognition: unknown

Theoretical and Numerical Efforts in Understanding Modern Experiments on Quantum Magnetism

Zi Yang Meng , Cristian D. Batista , Shiliang Li
Authors on Pith no claims yet

Pith reviewed 2026-05-10 07:14 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords quantum magnetismquantum spin liquidsnumerical simulationsanalytical methodsmaterials synthesisexotic phasesquantum phase transitions
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The pith

Quantum magnetism research advances when numerical simulations, analytical methods and experiments are treated as equal partners rather than one dominating the others.

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

The paper reviews progress on quantum magnets that exhibit exotic phases such as quantum spin liquids and unconventional phase transitions. It observes that specialists in numerical simulations, analytical theory, and materials experiments each tend to view their own pillar as the main driver, with the others mainly serving as checks. The authors argue instead for an integrated approach in which all three shape the core scientific questions, and they state that this shift has already begun to improve understanding of several key quantum magnetic models and their real-world material counterparts.

Core claim

The central claim is that a more integrated mindset, in which numerical simulations, analytical methods, and materials synthesis and experiments all actively shape the scientific narrative rather than one serving the others, has already started to advance the understanding of several important quantum magnetic models and their materials realizations.

What carries the argument

The integrated approach to the three pillars of numerical simulations, analytical methods, and materials synthesis/experiments, in which none is regarded as primary.

If this is right

  • Quantum phase transitions and spin-liquid states in frustrated magnets become clearer when simulation, theory, and experiment are combined from the start.
  • Materials candidates for exotic magnetic states are more reliably identified and characterized.
  • Persistent challenges in the field, such as the nature of certain quantum critical points, are more likely to be resolved through joint efforts.

Where Pith is reading between the lines

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

  • The same integrated pattern may apply to neighboring areas such as quantum materials beyond magnetism or strongly correlated electrons.
  • Future model building could routinely begin with joint constraints from all three pillars rather than sequential validation.
  • Educational programs in condensed-matter physics might benefit from training that emphasizes cross-pillar collaboration early.

Load-bearing premise

That the perception of one pillar dominating the others is common among researchers and that moving to an integrated approach is both possible and the main reason for recent advances.

What would settle it

A broad survey of active researchers in the field showing that the majority do not view their own specialty as primary, or concrete case studies demonstrating that recent advances in specific quantum magnet models occurred without meaningful integration across the three pillars.

Figures

Figures reproduced from arXiv: 2604.16820 by Cristian D. Batista, Shiliang Li, Zi Yang Meng.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

In recent decades, the study of quantum magnets, which feature unconventional behaviour such as exotic quantum phase transitions and quantum spin liquids, and unconventional magnetic states of matter, has made remarkable progress. However, each of the three foundational pillars -- numerical simulations, analytical methods, and, to a lesser extent, materials synthesis and experiments -- often tends to view itself as the primary driver of the field. Even through the need for collaboration among theory, numerics and experiment to understand the complex phases of quantum magnets is well established, yet, in our view there remains a persistent perception from experts in one area that the other two serve merely as supporting tool, primarily useful for validating the dominant ideas of one specialty, and less relevant to shaping the underlying scientific narrative. In this article, we advocate for a different, more integrated approach to overcome the challenges faced by quantum magnetism researchers. We argue that this alternative mindset has already started to advance the understanding of several important quantum magnetic models and their materials realizations.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 0 minor

Summary. The manuscript is a perspective article on quantum magnetism that describes progress in studying exotic phases such as quantum spin liquids and unconventional transitions. It notes that numerical simulations, analytical methods, and experiments each tend to position themselves as the primary driver, with the others seen as supporting tools. The central argument is that an integrated mindset across these pillars is needed to overcome challenges and has already begun advancing understanding of important models and their material realizations.

Significance. If the advocated shift toward integration proves effective, the perspective could encourage more collaborative work that combines numerical, analytical, and experimental insights, potentially accelerating progress on complex quantum magnetic states where isolated approaches have limitations.

major comments (1)
  1. [Abstract] Abstract: The assertion that the integrated mindset 'has already started to advance the understanding of several important quantum magnetic models and their materials realizations' is presented as the paper's key takeaway but is not supported by any concrete examples, specific models, mechanisms, or citations to recent advances within the provided text. This leaves the central claim as an interpretive opinion without falsifiable or verifiable grounding.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive report and for highlighting the need to better ground our central claim. We address the major comment below and have revised the manuscript to incorporate concrete examples and citations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the integrated mindset 'has already started to advance the understanding of several important quantum magnetic models and their materials realizations' is presented as the paper's key takeaway but is not supported by any concrete examples, specific models, mechanisms, or citations to recent advances within the provided text. This leaves the central claim as an interpretive opinion without falsifiable or verifiable grounding.

    Authors: We acknowledge that the abstract, as currently written, states the claim without explicit examples or citations, which can make it read as an unsupported opinion. The body of the manuscript does discuss how integrated numerical-analytical-experimental efforts have contributed to specific cases, but we agree this is not sufficiently highlighted to support the abstract's assertion. In the revised version we will add a brief sentence to the abstract referencing concrete examples (e.g., combined studies of the kagome-lattice Heisenberg antiferromagnet and certain frustrated triangular-lattice materials) together with key recent citations. This will provide verifiable grounding while preserving the perspective character of the article. revision: yes

Circularity Check

0 steps flagged

No circularity: perspective article with no derivations or quantitative claims

full rationale

The manuscript is a perspective advocating an integrated mindset across numerical, analytical, and experimental approaches in quantum magnetism. It presents no equations, derivations, fitted parameters, or new quantitative results. The central claim is an interpretive argument referencing existing literature rather than reducing any result to its own inputs by construction. No self-citation chains, ansatzes, or renamings of known results are load-bearing in a technical sense. This is a standard non-finding for opinion/perspective pieces that contain no formal derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper draws on established concepts in quantum magnetism without introducing new mathematical parameters, axioms, or postulated entities.

pith-pipeline@v0.9.0 · 5470 in / 954 out tokens · 55324 ms · 2026-05-10T07:14:48.876237+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

79 extracted references · 41 canonical work pages · 1 internal anchor

  1. [1]

    Haldane, F. D. M. ’luttinger liquid theory’ of one- dimensional quantum fluids. i. properties of the luttinger model and their extension to the general 1d interacting spinless fermi gas.Journal of Physics C: Solid State Physics14, 2585 (1981). URLhttps://doi.org/10. 1088/0022-3719/14/19/010

    1981

  2. [2]

    A., Frost, C

    Lake, B., Tennant, D. A., Frost, C. D. & Nagler, S. E. Quantum criticality and universal scaling of a quantum antiferromagnet.Nature Materials4, 329 – 334 (2005). URLhttps://doi.org/10.1038/nmat1327

    work page doi:10.1038/nmat1327 2005

  3. [3]

    URLhttps://www.science

    Coldea, R.et al.Quantum criticality in an ising chain: Experimental evidence for emergent E8 symmetry.Sci- ence327, 177–180 (2010). URLhttps://www.science. org/doi/abs/10.1126/science.1180085

    work page doi:10.1126/science.1180085 2010

  4. [4]

    A., Frost, C

    Lake, B., Tennant, D. A., Frost, C. D. & Nagler, S. E. Quantum criticality and universal scaling of a quantum antiferromagnet.Phys. Rev. Lett.111, 137205 (2013)

    2013

  5. [5]

    Mourigal, M.et al.Fractional spinon excitations in the quantum heisenberg antiferromagnetic chain.Nature Physics9, 435–441 (2013)

    2013

  6. [6]

    Shao, H.et al.Nearly deconfined spinon excitations in the square-lattice spin-1/2heisenberg antiferromagnet. Phys. Rev. X7, 041072 (2017). URLhttps://link. aps.org/doi/10.1103/PhysRevX.7.041072

    work page doi:10.1103/physrevx.7.041072 2017

  7. [7]

    & Verstraete, F

    Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and op- timization with matrix product states.Phys. Rev. B 94, 165116 (2016). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.94.165116

    work page doi:10.1103/physrevb.94.165116 2016

  8. [8]

    & Balents, L

    Savary, L. & Balents, L. Quantum spin liquids: A review. Rep. Prog. Phys.80, 016502 (2017). URLhttp://dx. doi.org/10.1088/0034-4885/80/1/016502

    work page doi:10.1088/0034-4885/80/1/016502 2017

  9. [9]

    & Moessner, R

    Knolle, J. & Moessner, R. A field guide to spin liquids. Annual Review of Condensed Matter Physics10, 451– 472 (2019)

    2019

  10. [10]

    W., Scheie, A

    Villanova, J. W., Scheie, A. O., Tennant, D. A., Okamoto, S. & Berlijn, T. First-principles deriva- tion of magnetic interactions in the triangular quan- tum spin liquid candidatesKYbCh 2(Ch=S,Se,Te) and AYbSe 2(A=Na,Rb).Phys. Rev. Res.5, 033050 (2023). URLhttps://link.aps.org/doi/10. 1103/PhysRevResearch.5.033050

    2023

  11. [11]

    Liu, J.et al.Gapless spin liquid behavior in a kagome heisenberg antiferromagnet with randomly dis- tributed hexagons of alternate bonds.Phys. Rev. B105, 024418 (2022). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.105.024418

    2022

  12. [12]

    Mater.8, 10 (2022)

    Hering, M.et al.Phasediagramofadistortedkagomean- tiferromagnet and application to Y-kapellasite.npj Com- put. Mater.8, 10 (2022)

    2022

  13. [13]

    Li , author Y

    Li, H.et al.Kosterlitz-thouless melting of magnetic or- der in the triangular quantum ising material tmmggao4. Nature Communications11, 1111 (2020). URLhttps: //doi.org/10.1038/s41467-020-14907-8

    work page doi:10.1038/s41467-020-14907-8 2020

  14. [14]

    URLhttps: //doi.org/10.1038/s41467-019-12410-3

    Shen, Y.et al.Intertwined dipolar and multipolar or- der in the triangular-lattice magnet tmmggao4.Na- ture Communications10, 4530 (2019). URLhttps: //doi.org/10.1038/s41467-019-12410-3

    work page doi:10.1038/s41467-019-12410-3 2019

  15. [15]

    URLhttps://doi.org/10

    Hu, Z.et al.Evidence of the berezinskii-kosterlitz- thouless phase in a frustrated magnet.Nature Commu- nications11, 5631 (2020). URLhttps://doi.org/10. 1038/s41467-020-19380-x

    2020

  16. [16]

    Da Liao, Y.et al.Phase diagram of the quantum ising model on a triangular lattice under external field.Phys. Rev. B103, 104416 (2021). URLhttps://link.aps. org/doi/10.1103/PhysRevB.103.104416

    work page doi:10.1103/physrevb.103.104416 2021

  17. [17]

    A., Stolze, K., Kong, T

    Cevallos, F. A., Stolze, K., Kong, T. & Cava, R. Anisotropic magnetic properties of the trian- gular plane lattice material tmmggao4.Materi- als Research Bulletin105, 154–158 (2018). URL https://www.sciencedirect.com/science/article/ pii/S0025540817339958

    2018

  18. [18]

    Li, Y.et al.Partial up-up-down order with the con- tinuously distributed order parameter in the triangu- lar antiferromagnettmmggao 4.Phys. Rev. X10, 011007 (2020). URLhttps://link.aps.org/doi/10. 1103/PhysRevX.10.011007

    2020

  19. [19]

    Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet.Phys. Rev. B68, 104409 (2003). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.68.104409

    work page doi:10.1103/physrevb.68.104409 2003

  20. [20]

    & Imada, M

    Kaneko, R., Morita, S. & Imada, M. Gapless spin- liquid phase in an extended spin 1/2 triangular heisen- berg model.Journal of the Physical Society of Japan83, 093707 (2014). URLhttps://doi.org/10.7566/JPSJ. 83.093707. https://doi.org/10.7566/JPSJ.83.093707

    work page doi:10.7566/jpsj 2014

  21. [21]

    Zhu \ and\ author S

    Zhu, Z. & White, S. R. Spin liquid phase of the s= 1 2 J1 −J 2 heisenberg model on the triangular lat- tice.Phys. Rev. B92, 041105 (2015). URLhttps: //link.aps.org/doi/10.1103/PhysRevB.92.041105

    work page doi:10.1103/physrevb.92.041105 2015

  22. [22]

    & Sheng, D

    Hu, W.-J., Gong, S.-S., Zhu, W. & Sheng, D. N. Competing spin-liquid states in the spin- 1 2 heisenberg model on the triangular lattice.Phys. Rev. B92, 140403 (2015). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.92.140403

    2015

  23. [23]

    & Becca, F

    Iqbal, Y., Hu, W.-J., Thomale, R., Poilblanc, D. & Becca, F. Spin liquid nature in the heisenberg J1 −J 2 triangular antiferromagnet.Phys. Rev. B93, 144411 (2016). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.93.144411

    2016

  24. [24]

    Saadatmand, S. N. & McCulloch, I. P. Symmetry fractionalization in the topological phase of the spin-1 2 J1−J2 triangular heisenberg model.Phys. Rev. B94, 121111 (2016). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.94.121111

    2016

  25. [25]

    Zhu , author P

    Zhu, Z., Maksimov, P. A., White, S. R. & Chernyshev, A. L. Topography of spin liquids on a triangular lat- tice.Phys. Rev. Lett.120, 207203 (2018). URLhttps:// link.aps.org/doi/10.1103/PhysRevLett.120.207203

    work page doi:10.1103/physrevlett.120.207203 2018

  26. [26]

    Macdougal, D.et al.Avoided quasiparticle decay and enhanced excitation continuum in the spin-1 2 near- heisenberg triangular antiferromagnetba3cosb2o9.Phys. 10 Rev. B102, 064421 (2020). URLhttps://link.aps. org/doi/10.1103/PhysRevB.102.064421

    work page doi:10.1103/physrevb.102.064421 2020

  27. [27]

    A.et al.Evidence of two-spinon bound states in the magnetic spectrum ofba3cosb2o9.Phys

    Ghioldi, E. A.et al.Evidence of two-spinon bound states in the magnetic spectrum ofba3cosb2o9.Phys. Rev. B 106, 064418 (2022). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.106.064418

    work page doi:10.1103/physrevb.106.064418 2022

  28. [28]

    O.et al.Proximate spin liquid and fractional- ization in the triangular antiferromagnet kybse2.Nature Physics20, 74 – 81 (2024)

    Scheie, A. O.et al.Proximate spin liquid and fractional- ization in the triangular antiferromagnet kybse2.Nature Physics20, 74 – 81 (2024). URLhttps://doi.org/10. 1038/s41567-023-02259-1

    2024

  29. [29]

    Resonating valence bonds: A new kind of insulator?Materials Research Bulletin8, 153– 160 (1973)

    Anderson, P. Resonating valence bonds: A new kind of insulator?Materials Research Bulletin8, 153– 160 (1973). URLhttps://www.sciencedirect.com/ science/article/pii/0025540873901670

    work page arXiv 1973

  30. [30]

    Zheng , author J

    Zheng, W., Fjærestad, J. O., Singh, R. R. P., McKenzie, R. H. & Coldea, R. Excitation spectra of the spin- 1 2 triangular-lattice heisenberg antiferromagnet.Phys. Rev. B74, 224420 (2006). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.74.224420

    work page doi:10.1103/physrevb.74.224420 2006

  31. [31]

    Simplevariationalwavefunctions for two-dimensional heisenberg spin-½antiferromagnets

    Huse, D.A.&Elser, V. Simplevariationalwavefunctions for two-dimensional heisenberg spin-½antiferromagnets. Phys. Rev. Lett.60, 2531–2534 (1988). URLhttps:// link.aps.org/doi/10.1103/PhysRevLett.60.2531

    work page doi:10.1103/physrevlett.60.2531 1988

  32. [32]

    & Pierre, L

    Bernu, B., Lhuillier, C. & Pierre, L. Signature of néel order in exact spectra of quantum antiferromag- nets on finite lattices.Phys. Rev. Lett.69, 2590– 2593 (1992). URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.69.2590

    1992

  33. [33]

    Capriotti, L., Trumper, A. E. & Sorella, S. Long-range néel order in the triangular heisenberg model.Phys. Rev. Lett.82, 3899–3902 (1999). URLhttps://link.aps. org/doi/10.1103/PhysRevLett.82.3899

    work page doi:10.1103/physrevlett.82.3899 1999

  34. [34]

    A., Chubukov, A

    Starykh, O. A., Chubukov, A. V. & Abanov, A. G. Flat spin-wave dispersion in a triangular antiferromag- net.Phys. Rev. B74, 180403 (2006). URLhttps: //link.aps.org/doi/10.1103/PhysRevB.74.180403

    work page doi:10.1103/physrevb.74.180403 2006

  35. [35]

    Zhitomirsky, M. E. & Chernyshev, A. L. Colloquium: Spontaneous magnon decays.Rev. Mod. Phys.85, 219– 242 (2013). URLhttps://link.aps.org/doi/10.1103/ RevModPhys.85.219

    2013

  36. [36]

    & Sachdev, S

    Read, N. & Sachdev, S. Large-n expansion for frus- trated quantum antiferromagnets.Phys. Rev. Lett.66, 1773–1776 (1991). URLhttps://link.aps.org/doi/ 10.1103/PhysRevLett.66.1773

    work page doi:10.1103/physrevlett.66.1773 1991

  37. [37]

    Natural flavor conservation in higgs induced neutral currents and the quark mixing angles,

    Chubukov, A. V., Sachdev, S. & Senthil, T. Quan- tum phase transitions in frustrated quantum an- tiferromagnets.Nuclear Physics B426, 601– 643 (1994). URLhttps://www.sciencedirect.com/ science/article/pii/055032139490023X

    work page arXiv 1994

  38. [38]

    Ma, J.et al.Static and dynamical properties of the spin-1/2equilateral triangular-lattice antiferro- magnetba 3cosb2o9.Phys. Rev. Lett.116, 087201 (2016). URLhttps://link.aps.org/doi/10.1103/ PhysRevLett.116.087201

    2016

  39. [39]

    Ito , author N

    Ito, S.et al.Structure of the magnetic excitations in the spin-1/2 triangular-lattice heisenberg antiferromag- net ba3cosb2o9.Nature Communications8, 235 (2017). URLhttps://doi.org/10.1038/s41467-017-00316-x

    work page doi:10.1038/s41467-017-00316-x 2017

  40. [40]

    Nature Communications9, 2666 (2018)

    Kamiya, Y.et al.The nature of spin excitations in the one-third magnetization plateau phase of ba3cosb2o9. Nature Communications9, 2666 (2018). URLhttps: //doi.org/10.1038/s41467-018-04914-1

    work page doi:10.1038/s41467-018-04914-1 2018

  41. [41]

    Arovas, D. P. & Auerbach, A. Functional integral theories of low-dimensional quantum heisenberg mod- els.Phys. Rev. B38, 316–332 (1988). URLhttps: //link.aps.org/doi/10.1103/PhysRevB.38.316

    work page doi:10.1103/physrevb.38.316 1988

  42. [42]

    A.et al.Dynamical structure factor of the triangular antiferromagnet: Schwinger boson the- ory beyond mean field.Phys

    Ghioldi, E. A.et al.Dynamical structure factor of the triangular antiferromagnet: Schwinger boson the- ory beyond mean field.Phys. Rev. B98, 184403 (2018). URLhttps://link.aps.org/doi/10.1103/ PhysRevB.98.184403

    2018

  43. [43]

    npj Quantum Materials8, 48 (2023)

    Xie, T.et al.Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet csybse2. npj Quantum Materials8, 48 (2023)

    2023

  44. [44]

    O.et al.Spectrum and low-energy gap in triangular quantum spin liquid NaYbSe2.arXiv e-prints arXiv:2406.17773 (2024)

    Scheie, A. O.et al.Spectrum and low-energy gap in triangular quantum spin liquid NaYbSe2.arXiv e-prints arXiv:2406.17773 (2024). 2406.17773

    work page arXiv 2024

  45. [45]

    P.et al.Gapped low energy excitations across an entanglement percolation transition in the quantum spin liquid candidate naybse2 (2024)

    Cairns, L. P.et al.Gapped low energy excitations across an entanglement percolation transition in the quantum spin liquid candidate naybse2 (2024). URLhttps:// arxiv.org/abs/2407.04695. 2407.04695

    work page arXiv 2024

  46. [46]

    Kagome´- and triangular-lattice heisen- berg antiferromagnets: Ordering from quantum fluctu- ations and quantum-disordered ground states with un- confined bosonic spinons.Phys

    Sachdev, S. Kagome´- and triangular-lattice heisen- berg antiferromagnets: Ordering from quantum fluctu- ations and quantum-disordered ground states with un- confined bosonic spinons.Phys. Rev. B45, 12377– 12396 (1992). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.45.12377

    1992

  47. [47]

    & Vishwanath, A

    Wang, F. & Vishwanath, A. Spin-liquid states on the triangular and kagomé lattices: A projective-symmetry- group analysis of schwinger boson states.Phys. Rev. B 74, 174423 (2006). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.74.174423

    work page doi:10.1103/physrevb.74.174423 2006

  48. [48]

    & Sachdev, S

    Shackleton, H. & Sachdev, S. Sign-problem-free effective models of triangular lattice quantum antiferromagnets. Phys. Rev. B111, 075101 (2025). URLhttps://link. aps.org/doi/10.1103/PhysRevB.111.075101

    work page doi:10.1103/physrevb.111.075101 2025

  49. [49]

    Science372, 276–279 (2021)

    Miksch, B.et al.Gapped magnetic ground state in quan- tum spin liquid candidateκ-(BEDT-TTF) 2Cu2(CN)3. Science372, 276–279 (2021). URLhttps://www. science.org/doi/abs/10.1126/science.abc6363

    work page doi:10.1126/science.abc6363 2021

  50. [50]

    Seifert, U. F. P., Willsher, J., Drescher, M., Pollmann, F. & Knolle, J. Spin-peierls instability of the u(1) dirac spin liquid.Nature Communications15, 7110 (2024). URL https://doi.org/10.1038/s41467-024-51367-w

    work page doi:10.1038/s41467-024-51367-w 2024

  51. [51]

    Szasz, A., Motruk, J., Zaletel, M. P. & Moore, J. E. Chiral Spin Liquid Phase of the Triangular Lattice Hubbard Model: A Density Matrix Renor- malization Group Study.Physical Review X10, 021042 (2020). URLhttps://link.aps.org/doi/10. 1103/PhysRevX.10.021042. Publisher: American Physi- cal Society

    2020

  52. [52]

    Ma, Z.et al.Spin-glass ground state in a triangular- lattice compoundybzngao 4.Phys. Rev. Lett.120, 087201 (2018). URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.120.087201

    2018

  53. [53]

    & Mi, J.-X

    Chen, X.-H., Huang, Y.-X., Pan, Y. & Mi, J.-X. Quan- tum spin liquid candidate YCu3(OH)6Br2[Brx(OH)1−x] (x≈0.51): With an almost perfect kagomé layer.J. Magn. Magn. Mater.512, 167066 (2020)

    2020

  54. [54]

    Norman, M. R. Colloquium: Herbertsmithite and the search for the quantum spin liquid.Rev. Mod. Phys.88, 041002 (2016)

    2016

  55. [55]

    URLhttps://doi.org/10.1038/ s41567-024-02495-z

    Zeng, Z.et al.Spectral evidence for dirac spinons in a kagome lattice antiferromagnet.Nature Physics20, 1097 – 1102 (2024). URLhttps://doi.org/10.1038/ s41567-024-02495-z

    2024

  56. [56]

    Han, L.et al.Spin excitations arising from anisotropic dirac spinons inYCu 3(OD)6Br2[Br0.33(OD)0.67].Phys. 11 Rev. B112, 045114 (2025). URLhttps://link.aps. org/doi/10.1103/qypv-n4yg

    work page doi:10.1103/qypv-n4yg 2025

  57. [57]

    URLhttps://doi.org/10.1038/ nature11659

    Han, T.-H.et al.Fractionalized excitations in the spin- liquid state of a kagome-lattice antiferromagnet.Nature 492, 406 – 410 (2012). URLhttps://doi.org/10.1038/ nature11659

    2012

  58. [58]

    Feng, Z.et al.Gapped spin-1/2 spinon excita- tions in a new kagome quantum spin liquid com- pound Cu3Zn(OH)6FBr.Chin. Phys. Lett.34, 077502 (2017). URLhttp://cpl.iphy.ac.cn/EN/abstract/ article_70811.shtml

    2017

  59. [59]

    Nature Physics16, 469 – 474 (2020)

    Khuntia, P.et al.Gapless ground state in the archety- pal quantum kagome antiferromagnet ZnCu3(OH)6Cl2. Nature Physics16, 469 – 474 (2020). URLhttps: //doi.org/10.1038/s41567-020-0792-1

    work page doi:10.1038/s41567-020-0792-1 2020

  60. [60]

    J., de Vries, M

    Nilsen, G. J., de Vries, M. A., Stewart, J. R., Harrison, A. & Rϕnnow, H. M. Low-energy spin dynamics of the s = 1/2 kagome system herbertsmithite.J. Phys.: Condens. Matter25, 106001 (2013)

    2013

  61. [61]

    URLhttp:// cpl.iphy.ac.cn/EN/abstract/article_115989.shtml

    Wei, Y.et al.Nonlocal effects of low-energy excitations in quantum-spin-liquid candidate Cu3Zn(OH)6FBr.Chi- nese Physics Letters38, 097501 (2021). URLhttp:// cpl.iphy.ac.cn/EN/abstract/article_115989.shtml

    2021

  62. [62]

    Zeng, Z.et al.Possible dirac quantum spin liquid in the kagome quantum antiferromagnet YCu3(OH)6Br2[Brx(OH)1−x].Phys. Rev. B105, L121109 (2022). URLhttps://link.aps.org/doi/10. 1103/PhysRevB.105.L121109

    2022

  63. [63]

    Phys.20, 435–441 (2024)

    Jeon, S.et al.One-ninthmagnetizationplateaustabilized by spin entanglement in a kagome antiferromagnet.Nat. Phys.20, 435–441 (2024)

    2024

  64. [64]

    Ran, Y., Hermele, M., Lee, P. A. & Wen, X.-G. Projected-wave-function study of the spin-1/2heisen- berg model on the kagomé lattice.Phys. Rev. Lett.98, 117205 (2007). URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.98.117205

    2007

  65. [65]

    Chatterjee, D.et al.From spin liquid to mag- netic ordering in the anisotropic kagome Y-kapellasite Y3Cu9(OH)19Cl8: A single-crystal study.Phys. Rev. B 107, 125156 (2023). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.107.125156

    work page doi:10.1103/physrevb.107.125156 2023

  66. [66]

    Xu, A.et al.Magnetic ground states in the kagome systemYCu 3(OH)6[(ClxBr1−x)3−y(OH)y].Phys. Rev. B 110, 085146 (2024). URLhttps://link.aps.org/doi/ 10.1103/PhysRevB.110.085146

    work page doi:10.1103/physrevb.110.085146 2024

  67. [67]

    Yan, S., Huse, D. A. & White, S. R. Spin- liquid ground state of the <i>s</i> = 1/2 kagome heisenberg antiferromagnet.Science332, 1173–1176 (2011). URLhttps://www.science.org/doi/abs/10. 1126/science.1201080

    2011

  68. [68]

    Depenbrock, S., McCulloch, I. P. & Schollwöck, U. Na- ture of the spin-liquid ground state of thes= 1/2Heisen- berg model on the kagome lattice.Phys. Rev. Lett.109, 067201 (2012). URLhttps://link.aps.org/doi/10. 1103/PhysRevLett.109.067201

    2012

  69. [69]

    J.et al.Gapless spin-liquid ground state in thes= 1/2kagome antiferromagnet.Phys

    Liao, H. J.et al.Gapless spin-liquid ground state in thes= 1/2kagome antiferromagnet.Phys. Rev. Lett. 118, 137202 (2017). URLhttps://link.aps.org/doi/ 10.1103/PhysRevLett.118.137202

    work page doi:10.1103/physrevlett.118.137202 2017

  70. [70]

    Lett.42, 027504 (2025)

    Li, Z.et al.Antiferromagnetic order and possi- ble quantum spin liquid in kagome antiferromagnet LuCu3(OH)6Br2[Brx(OH)1−x].Chinese Phys. Lett.42, 027504 (2025)

    2025

  71. [71]

    Y.et al.Monte carlo study of lattice com- pact quantum electrodynamics with fermionic matter: The parent state of quantum phases.Phys

    Xu, X. Y.et al.Monte carlo study of lattice com- pact quantum electrodynamics with fermionic matter: The parent state of quantum phases.Phys. Rev. X9, 021022 (2019). URLhttps://link.aps.org/doi/10. 1103/PhysRevX.9.021022

    2019

  72. [72]

    Emergent gauge flux in mixed QED$_3$ with flavor chemical potential: application to magnetized U(1) Dirac spin liquids

    Chen, C.et al.Emergent gauge flux in QED3 with flavor chemical potential: application to magnetized U(1) Dirac spin liquids.arXiv e-printsarXiv:2508.08528 (2025). 2508.08528

    work page internal anchor Pith review arXiv 2025

  73. [73]

    Willsher and J

    Willsher, J. & Knolle, J. Dynamics and stability of u(1) spin liquids beyond mean-field theory: Triangular-lattice J1 −J 2 heisenberg model (2025). URLhttps://arxiv. org/abs/2503.13831. 2503.13831

    work page arXiv 2025

  74. [74]

    Anyons in an exactly solved model and beyond

    Kitaev, A. Anyons in an exactly solved model and beyond.Annals of Physics321, 2–111 (2006). URL https://doi.org/10.1016/j.aop.2005.10.005

    work page Pith review doi:10.1016/j.aop.2005.10.005 2006

  75. [75]

    & Khaliullin, G

    Jackeli, G. & Khaliullin, G. Mott insulators in the strong spin-orbit coupling limit: From heisenberg to a quan- tum compass and kitaev models.Physical Review Letters 102, 017205 (2009). URLhttps://doi.org/10.1103/ PhysRevLett.102.017205

    2009

  76. [76]

    & Hickey, C

    Trebst, S. & Hickey, C. Kitaev materials.Physics Re- ports950, 1–37 (2022). Comprehensive theoretical and experimental review of Kitaev materials

    2022

  77. [77]

    URLhttps: //arxiv.org/abs/2502.08698

    Möller, M.et al.The saga ofα−RuCl 3: Parame- ters, models, and phase diagrams (2025). URLhttps: //arxiv.org/abs/2502.08698. 2502.08698

    work page arXiv 2025

  78. [78]

    Matsuda, T

    Matsuda, Y., Shibauchi, T. & Kee, H.-Y. Kitaev Quan- tum Spin Liquids.arXiv e-printsarXiv:2501.05608 (2025). 2501.05608

    work page arXiv 2025

  79. [79]

    High precision analytical description of the allowed beta spectrum shape

    Kogut, J. B. An introduction to lattice gauge theory and spin systems.Reviews of Modern Physics51, 659–713 (1979). URLhttps://doi.org/10.1103/RevModPhys. 51.659. Acknowledgments ZYM thanks Chengkang Zhou for helping with making the figures and acknowledge the support from the Research Grants Council (RGC) of Hong Kong (Project Nos. AoE/P701/20, 17309822, ...

    work page doi:10.1103/revmodphys 1979