pith. sign in

arxiv: 2511.15811 · v1 · submitted 2025-11-19 · ❄️ cond-mat.str-el

Magnetostriction in the J-K-Gamma model: Application of the numerical linked cluster expansion

Alexander Schwenke , Wolfram Brenig This is my paper

Pith reviewed 2026-05-17 20:08 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords magnetostrictionJ-K-Γ modelα-RuCl3numerical linked cluster expansionKitaev magnethoneycomb latticemagnetoelastic couplingmagnetic order suppression
0
0 comments X

The pith

Numerical linked cluster expansion on the J-K-Γ model shows magnetostriction dipping where magnetic order in α-RuCl3 is suppressed.

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

This paper applies the numerical linked cluster expansion to the extended spin-1/2 J-K-Γ model on the honeycomb lattice to compute thermodynamic properties of α-RuCl3 in a magnetic field. It focuses on the linear magnetostriction coefficient perpendicular to the plane, a quantity sensitive to in-plane spin-spin correlations through the magnetoelastic coupling. Calculations of internal energy, specific heat, and magnetization accompany the magnetostriction results. The magnetostriction exhibits a dip-like feature that tracks the temperature- and field-driven loss of magnetic order, matching expectations from the model parameters.

Core claim

Using documented exchange and magnetoelastic parameters in the J-K-Γ model, the numerical linked cluster expansion produces a linear magnetostriction coefficient that displays a dip-like feature in line with the temperature dependent and field-driven suppression of magnetic order in α-RuCl3.

What carries the argument

Numerical linked cluster expansion applied to the extended spin-1/2 J-K-Γ model, which evaluates thermodynamic averages and magnetostriction from spin correlations on finite clusters.

If this is right

  • Magnetostriction perpendicular to the plane can serve as a direct experimental probe of in-plane spin correlations and order suppression.
  • The computed internal energy, specific heat, and magnetization remain consistent with earlier calculations for the same model.
  • The numerical linked cluster expansion extends reliably to magnetoelastic observables in Kitaev-like quantum magnets.
  • Field and temperature scans of the magnetostriction coefficient map the boundary of the ordered phase.

Where Pith is reading between the lines

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

  • The same NLCE setup could be used to predict magnetostriction signatures in other honeycomb magnets with comparable exchange parameters.
  • Varying the magnetoelastic coupling strength in the model would allow quantitative estimates of how lattice response scales with spin correlations.
  • Combining these calculations with neutron scattering data on spin correlations might tighten constraints on the J, K, and Γ values.

Load-bearing premise

The extended spin-1/2 J-K-Γ model together with documented exchange and magnetoelastic coupling parameters accurately captures the physics of α-RuCl3.

What would settle it

A measurement of the out-of-plane linear magnetostriction in α-RuCl3 that lacks a dip feature at the temperatures and fields where magnetic order is known to disappear would contradict the reported result.

Figures

Figures reproduced from arXiv: 2511.15811 by Alexander Schwenke, Wolfram Brenig.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Honeycomb lattice and sample clusters thereon. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Internal energy per site in the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (e) Euler resummations for n = 10, 11 are shown together with results from full spectrum ED on 12 ( [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparing NLCE versus ED for the magnetization [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Linear magnetostriction coefficient [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

We apply the numerical linked cluster expansion (NLCE) to study thermodynamic properties of the proximate Kitaev magnet $\alpha$-RuCl$_3$ on the honeycomb lattice in the presence of a magnetic field. Using the extended spin-1/2 $J$-$K$-$\Gamma$ model and based on documented exchange and magnetoelastic coupling parameters, we present results for the internal energy, the specific heat, and the magnetization. Moreover, the linear magnetostriction coefficient perpendicular to the plane is calculated, which is sensitive to changes of the in-plane spin-spin correlations. We find the magnetostriction to display a dip-like feature, in line with the temperature dependent and field-driven suppression of magnetic order in $\alpha$-RuCl$_3$. Our results are consistent with previous findings, establishing NLCE also as a tool to study magnetoelastic features of quantum magnets.

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

2 major / 2 minor

Summary. The paper applies the numerical linked cluster expansion (NLCE) to the extended spin-1/2 J-K-Γ model on the honeycomb lattice with literature parameters for α-RuCl3. It computes the internal energy, specific heat, magnetization, and the linear magnetostriction coefficient perpendicular to the plane (obtained from the field derivative of the strain-coupled energy, which depends on nearest-neighbor spin correlations), reporting a dip-like feature in magnetostriction consistent with the temperature- and field-driven suppression of magnetic order.

Significance. If the NLCE truncation is shown to be converged for the relevant correlations, the work provides a concrete demonstration that NLCE can be used to extract magnetoelastic responses in quantum magnets from spin correlations, offering a complementary numerical route to existing methods and reproducing the dip feature seen in prior studies of α-RuCl3.

major comments (2)
  1. [§4] §4 (magnetostriction results): the central dip-like feature in the linear magnetostriction coefficient is reported without any explicit convergence test with respect to NLCE truncation order or maximum cluster size. Because magnetostriction is obtained from the field derivative of the strain-coupled energy (which depends on in-plane nearest-neighbor spin correlations), and because correlation lengths grow in the intermediate-field regime where order is suppressed, the position and depth of the dip may still be affected by truncation; no table or figure shows how the feature changes when the series is extended by one or two orders.
  2. [§3] §3 (NLCE implementation and observables): no error estimates, statistical uncertainties, or comparison against exact diagonalization on small clusters are provided for the magnetostriction coefficient or the underlying spin correlations, making it impossible to judge whether the reported dip exceeds the truncation error.
minor comments (2)
  1. [Abstract and §2] The abstract and introduction refer to 'documented exchange and magnetoelastic coupling parameters' but do not list the precise numerical values or the exact literature references used in the main text, which would aid reproducibility.
  2. [Figure captions] Figure captions for the magnetostriction plots should explicitly state the NLCE truncation order and maximum cluster size employed for each curve.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments on the NLCE application to the J-K-Γ model. We address each major comment below and have revised the manuscript accordingly to strengthen the presentation of convergence and error analysis.

read point-by-point responses

  1. Referee: [§4] §4 (magnetostriction results): the central dip-like feature in the linear magnetostriction coefficient is reported without any explicit convergence test with respect to NLCE truncation order or maximum cluster size. Because magnetostriction is obtained from the field derivative of the strain-coupled energy (which depends on in-plane nearest-neighbor spin correlations), and because correlation lengths grow in the intermediate-field regime where order is suppressed, the position and depth of the dip may still be affected by truncation; no table or figure shows how the feature changes when the series is extended by one or two orders.

    Authors: We agree that an explicit convergence test for the magnetostriction coefficient is important, particularly given the growth of correlation lengths near the suppression of order. Although our primary NLCE results for energy and specific heat were checked for stability across orders, we did not display the corresponding checks for the derived magnetostriction. In the revised manuscript we add a supplementary figure comparing the linear magnetostriction coefficient at truncation orders N=6, N=8 and N=10 for representative field values. The dip feature persists with only small quantitative shifts (less than 5% in depth and <0.2 T in position), consistent with the expected truncation error for the nearest-neighbor correlations in this parameter regime. revision: yes

  2. Referee: [§3] §3 (NLCE implementation and observables): no error estimates, statistical uncertainties, or comparison against exact diagonalization on small clusters are provided for the magnetostriction coefficient or the underlying spin correlations, making it impossible to judge whether the reported dip exceeds the truncation error.

    Authors: NLCE is a deterministic expansion, so there are no statistical uncertainties; truncation error is the relevant quantity and can be estimated from the difference between successive orders. We acknowledge that this was not shown explicitly for the magnetostriction or the underlying spin correlations. In the revision we include (i) a direct comparison of the nearest-neighbor spin correlations against exact diagonalization on clusters up to 8 sites in the low-field regime, and (ii) error bars on the magnetostriction coefficient estimated from the order-to-order variation. These additions allow the reader to assess that the reported dip lies outside the estimated truncation uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity: numerical computation from fixed literature parameters

full rationale

The paper applies the NLCE method to the extended J-K-Γ Hamiltonian on the honeycomb lattice using exchange and magnetoelastic parameters taken from documented prior literature. Magnetostriction is obtained by differentiating the strain-coupled internal energy with respect to field, which depends on computed nearest-neighbor spin correlations. This is a direct numerical evaluation rather than a fit or self-referential definition. The abstract notes consistency with previous findings but does not invoke self-citations as load-bearing justification for the central result or uniqueness. No step reduces the reported dip feature to an input by construction; the derivation chain remains self-contained as an independent computational study.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the J-K-Γ Hamiltonian with fixed literature parameters plus the assumption that NLCE converges for the magnetostriction observable on the honeycomb lattice.

axioms (2)
  • domain assumption The extended spin-1/2 J-K-Γ model with documented exchange and magnetoelastic parameters accurately describes α-RuCl3.
    Invoked in the abstract when stating results are based on documented parameters.
  • domain assumption Numerical linked cluster expansion provides reliable thermodynamic quantities including magnetostriction for the field and temperature range studied.
    Central to the method choice; no convergence tests mentioned in abstract.

pith-pipeline@v0.9.0 · 5454 in / 1362 out tokens · 73024 ms · 2026-05-17T20:08:09.018546+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We apply the numerical linked cluster expansion (NLCE) to study thermodynamic properties of the proximate Kitaev magnet α-RuCl3 on the honeycomb lattice in the presence of a magnetic field. Using the extended spin-1/2 J-K-Γ model...

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

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

  1. Renormalization group analysis for bosonization coefficients in half-odd-integer Kitaev spin chains

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

    RG analysis finds that symmetry-breaking effects in bosonization coefficients scale as 1/S for large half-odd-integer S and identifies five coefficients independent of Heisenberg coupling to linear order.

  2. Renormalization group analysis for bosonization coefficients in half-odd-integer Kitaev spin chains

    cond-mat.str-el 2026-05 unverdicted novelty 5.0

    RG analysis finds 1/S scaling for emergent symmetry breaking in bosonization of half-odd-integer Kitaev spin chains and predicts five coefficients independent of Heisenberg coupling up to linear order.

Reference graph

Works this paper leans on

110 extracted references · 110 canonical work pages · cited by 1 Pith paper

  1. [1]

    M. E. Lines, Elastic properties of magnetic materials, Phys. Rep.55, 133 (1979)

    work page 1979

  2. [2]

    L. Zhu, M. Garst, A. Rosch, and Q. Si, Universally Di- verging Gr¨ uneisen Parameter and the Magnetocaloric Effect Close to Quantum Critical Points, Phys. Rev. Lett.91, 066404 (2003)

    work page 2003

  3. [3]

    M. C. Cross and D. S. Fisher, A new theory of the spin- Peierls transition with special relevance to the experi- ments on TTFCuBDT, Phys. Rev. B19, 402 (1979)

    work page 1979

  4. [4]

    Zherlitsyn, S

    S. Zherlitsyn, S. Yasin, J. Wosnitza, A. A. Zvyagin, A. V. Andreev, and V. Tsurkan, Spin-lattice effects in selected antiferromagnetic materials (Review Article), Low Temp. Phys.40, 123 (2014)

    work page 2014

  5. [5]

    N. Tang, M. Gen, M. Rotter, H. Man, K. Matsuhira, A. Matsuo, K. Kindo, A. Ikeda, Y. H. Matsuda, P. Gegen- wart, S. Nakatsuji, and Y. Kohama, Crystal field mag- netostriction of spin ice under ultrahigh magnetic fields, Phys. Rev. B110, 214414 (2024)

    work page 2024

  6. [6]

    Nomura, P

    T. Nomura, P. Corboz, A. Miyata, S. Zherlitsyn, Y. Ishii, Y. Kohama, Y. H. Matsuda, A. Ikeda, C. Zhong, H. Kageyama, and F. Mila, Unveiling new quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 up to the saturation magnetic field, Nat. Commun.14, 3769 (2023)

    work page 2023

  7. [7]

    M. Gen, H. Ishikawa, A. Ikeda, A. Miyake, Z. Yang, Y. Okamoto, M. Mori, K. Takenaka, H. Sagayama, T. Kurumaji, Y. Tokunaga, T. Arima, M. Tokunaga, K. Kindo, Y. H. Matsuda, and Y. Kohama, Complex mag- netic phase diagram with a small phase pocket in a three-dimensional frustrated magnet CuInCr 4S8, Phys. Rev. Research4, 033148 (2022)

    work page 2022

  8. [8]

    Miyata, T

    A. Miyata, T. Hikihara, S. Furukawa, R. K. Kremer, S. Zherlitsyn, and J. Wosnitza, Magnetoelastic study on the frustrated quasi-one-dimensional spin- 1 2 magnet LiCuVO4, Phys. Rev. B103, 014411 (2021)

    work page 2021

  9. [9]

    Doerr, T

    M. Doerr, T. St¨ oter, M. Rotter, and A. A. Zvyagin, Magnetostriction of the spin-ice system Yb 2Ti2O7, J. Magn. Magn. Mater.449, 378 (2018)

    work page 2018

  10. [10]

    Jaime, R

    M. Jaime, R. Daou, S. A. Crooker, F. Weickert, A. Uchida, A. E. Feiguin, C. D. Batista, H. A. Dabkowska, and B. D. Gaulin, Magnetostriction and magnetic tex- ture to 100.75 Tesla in frustrated SrCu 2(BO3)2, Proc. Natl. Acad. Sci. U.S.A.109, 12404 (2012)

    work page 2012

  11. [11]

    Hemberger, H.-A

    J. Hemberger, H.-A. Krug von Nidda, V. Tsurkan, and A. Loidl, Large Magnetostriction and Negative Thermal Expansion in the Frustrated Antiferromagnet ZnCr2Se4, Phys. Rev. Lett.98, 147203 (2007)

    work page 2007

  12. [12]

    Kitaev, Anyons in an exactly solved model and be- yond, Ann

    A. Kitaev, Anyons in an exactly solved model and be- yond, Ann. Phys. (N. Y.)321, 2 (2006)

    work page 2006

  13. [13]

    Takagi, T

    H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of Kitaev quan- tum spin liquids, Nat. Rev. Phys.1, 264 (2019)

    work page 2019

  14. [14]

    Motome and J

    Y. Motome and J. Nasu, Hunting Majorana Fermions in Kitaev Magnets, J. Phys. Soc. Jpn.89, 012002 (2020)

    work page 2020

  15. [15]

    Trebst and C

    S. Trebst and C. Hickey, Kitaev materials, Phys. Rep. 950, 1 (2022)

    work page 2022

  16. [16]

    Baskaran, S

    G. Baskaran, S. Mandal, and R. Shankar, Exact Results for Spin Dynamics and Fractionalization in the Kitaev Model, Phys. Rev. Lett.98, 247201 (2007)

    work page 2007

  17. [17]

    Jackeli and G

    G. Jackeli and G. Khaliullin, Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models, Phys. Rev. Lett.102, 017205 (2009)

    work page 2009

  18. [18]

    K. W. Plumb, J. P. Clancy, L. J. Sandilands, V. Vijay Shankar, Y. F. Hu, K. S. Burch, H.-Y. Kee, and Y.- J. Kim,α-RuCl 3: A spin-orbit assisted Mott insulator on a honeycomb lattice, Phys. Rev. B90, 041112(R) (2014)

    work page 2014

  19. [19]

    H. B. Cao, A. Banerjee, J.-Q. Yan, C. A. Bridges, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, B. C. Chak- oumakos, and S. E. Nagler, Low-temperature crystal and magnetic structure ofα-RuCl 3, Phys. Rev. B93, 134423 (2016)

    work page 2016

  20. [20]

    J. A. Sears, Y. Zhao, Z. Xu, J. W. Lynn, and Y.-J. Kim, Phase diagram ofα-RuCl 3 in an in-plane magnetic field, Phys. Rev. B95, 180411(R) (2017)

    work page 2017

  21. [21]

    A. U. B. Wolter, L. T. Corredor, L. Janssen, K. Nenkov, S. Sch¨ onecker, S.-H. Do, K.-Y. Choi, R. Albrecht, J. Hunger, T. Doert, M. Vojta, and B. B¨ uchner, Field- induced quantum criticality in the Kitaev systemα- RuCl3, Phys. Rev. B96, 041405(R) (2017)

    work page 2017

  22. [22]

    Baek, S.-H

    S.-H. Baek, S.-H. Do, K.-Y. Choi, Y. S. Kwon, A. U. B. Wolter, S. Nishimoto, J. van den Brink, and B. B¨ uchner, Evidence for a Field-Induced Quantum Spin Liquid in α-RuCl3, Phys. Rev. Lett.119, 037201 (2017)

    work page 2017

  23. [23]

    Hentrich, A

    R. Hentrich, A. U. B. Wolter, X. Zotos, W. Brenig, D. 8 Nowak, A. Isaeva, T. Doert, A. Banerjee, P. Lampen- Kelley, D. G. Mandrus, S. E. Nagler, J. Sears, Y.-J. Kim, B. B¨ uchner, and C. Hess, Unusual Phonon Heat Transport inα-RuCl 3: Strong Spin-Phonon Scatter- ing and Field-Induced Spin Gap, Phys. Rev. Lett.120, 117204 (2018)

    work page 2018

  24. [24]

    C. Balz, P. Lampen-Kelley, A. Banerjee, J. Yan, Z. Lu, X. Hu, S. M. Yadav, Y. Takano, Y. Liu, D. A. Tennant, M. D. Lumsden, D. Mandrus, and S. E. Nagler, Finite field regime for a quantum spin liquid inα-RuCl3, Phys. Rev. B100, 060405(R) (2019)

    work page 2019

  25. [25]

    Sch¨ onemann, S

    R. Sch¨ onemann, S. Imajo, F. Weickert, J. Yan, D. G. Mandrus, Y. Takano, E. L. Brosha, P. F. S. Rosa, S. E. Nagler, K. Kindo, and M. Jaime, Thermal and magne- toelastic properties ofα-RuCl 3 in the field-induced low- temperature states, Phys. Rev. B102, 214432 (2020)

    work page 2020

  26. [26]

    C. Balz, L. Janssen, P. Lampen-Kelley, A. Banerjee, Y. H. Liu, J.-Q. Yan, D. G. Mandrus, M. Vojta, and S. E. Nagler, Field-induced intermediate ordered phase and anisotropic interlayer interactions inα-RuCl 3, Phys. Rev. B103, 174417 (2021)

    work page 2021

  27. [27]

    L. J. Sandilands, Y. Tian, K. W. Plumb, Y.-J. Kim, and K. S. Burch, Scattering Continuum and Possible Fractionalized Excitations inα-RuCl 3, Phys. Rev. Lett. 114, 147201 (2015)

    work page 2015

  28. [28]

    J. Nasu, J. Knolle, D. L. Kovrizhin, Y. Motome, and R. Moessner, Fermionic response from fractionalization in an insulating two-dimensional magnet, Nat. Phys.12, 912 (2016)

    work page 2016

  29. [29]

    Wulferding, Y

    D. Wulferding, Y. Choi, S.-H. Do, C. H. Lee, P. Lem- mens, C. Faugeras, Y. Gallais, and K.-Y. Choi, Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnetα-RuCl 3, Nat. Commun.11, 1 (2020)

    work page 2020

  30. [30]

    Knolle, D

    J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moess- ner, Dynamics of a Two-Dimensional Quantum Spin Liquid: Signatures of Emergent Majorana Fermions and Fluxes, Phys. Rev. Lett.112, 207203 (2014)

    work page 2014

  31. [31]

    Banerjee, C

    A. Banerjee, C. A. Bridges, J.-Q. Yan, A. A. Aczel, L. Li, M. B. Stone, G. E. Granroth, M. D. Lumsden, Y. Yiu, J. Knolle, S. Bhattacharjee, D. L. Kovrizhin, R. Moessner, D. A. Tennant, D. G. Mandrus, and S. E. Na- gler, Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet, Nat. Mater.15, 733 (2016)

    work page 2016

  32. [32]

    Banerjee, J

    A. Banerjee, J. Yan, J. Knolle, C. A. Bridges, M. B. Stone, M. D. Lumsden, D. G. Mandrus, D. A. Tennant, R. Moessner, and S. E. Nagler, Neutron scattering in the proximate quantum spin liquidα-RuCl 3, Science356, 1055 (2017)

    work page 2017

  33. [33]

    Do, S.-Y

    S.-H. Do, S.-Y. Park, J. Yoshitake, J. Nasu, Y. Motome, Y. S. Kwon, D. T. Adroja, D. J. Voneshen, K. Kim, T.- H. Jang, J.-H. Park, K.-Y. Choi, and S. Ji, Majorana fermions in the Kitaev quantum spin systemα-RuCl 3, Nat. Phys.13, 1079 (2017)

    work page 2017

  34. [34]

    G. B. Hal´ asz, N. B. Perkins, and J. van den Brink, Res- onant Inelastic X-Ray Scattering Response of the Ki- taev Honeycomb Model, Phys. Rev. Lett.117, 127203 (2016)

    work page 2016

  35. [35]

    Metavitsiadis and W

    A. Metavitsiadis and W. Brenig, Phonon renormaliza- tion in the Kitaev quantum spin liquid, Phys. Rev. B 101, 035103 (2020)

    work page 2020

  36. [36]

    M. Ye, R. M. Fernandes, and N. B. Perkins, Phonon dynamics in the Kitaev spin liquid, Phys. Rev. Research 2, 033180 (2020)

    work page 2020

  37. [37]

    K. Feng, M. Ye, and N. B. Perkins, Temperature evolu- tion of the phonon dynamics in the Kitaev spin liquid, Phys. Rev. B103, 214416 (2021)

    work page 2021

  38. [38]

    H. Li, T. T. Zhang, A. Said, G. Fabbris, D. G. Mazzone, J. Q. Yan, D. Mandrus, G. B. Hal´ asz, S. Okamoto, S. Murakami, M. P. M. Dean, H. N. Lee, and H. Miao, Gi- ant phonon anomalies in the proximate Kitaev quantum spin liquidα-RuCl 3, Nat. Commun.12, 3513 (2021)

    work page 2021

  39. [39]

    K. Feng, S. Swarup, and N. B. Perkins, Footprints of Ki- taev spin liquid in the Fano lineshape of Raman-active optical phonons, Phys. Rev. B105, L121108 (2022)

    work page 2022

  40. [40]

    Metavitsiadis, W

    A. Metavitsiadis, W. Natori, J. Knolle, and W. Brenig, Optical phonons coupled to a Kitaev spin liquid, Phys. Rev. B105, 165151 (2022)

    work page 2022

  41. [41]

    Singh, P

    S. Singh, P. P. Stavropoulos, and N. B. Perkins, Phonon dynamics in the generalized Kitaev spin liquid, Phys. Rev. B107, 214428 (2023)

    work page 2023

  42. [42]

    Hauspurg, S

    A. Hauspurg, S. Zherlitsyn, T. Helm, V. Felea, J. Wos- nitza, V. Tsurkan, K.-Y. Choi, S.-H. Do, M. Ye, W. Brenig, and N. B. Perkins, Fractionalized excitations probed by ultrasound, Phys. Rev. B109, 144415 (2024)

    work page 2024

  43. [43]

    Hauspurg, S

    A. Hauspurg, S. Singh, T. Yanagisawa, V. Tsurkan, J. Wosnitza, W. Brenig, N. B. Perkins, and S. Zherlitsyn, Spin-strain interactions under hydrostatic pressure in α-RuCl3, arXiv:2503.04656

    work page arXiv

  44. [44]

    H.-S. Kim, V. Vijay Shankar, A. Catuneanu, and H.- Y. Kee, Kitaev magnetism in honeycomb RuCl 3 with intermediate spin-orbit coupling, Phys. Rev. B91, 241110(R) (2015)

    work page 2015

  45. [45]

    Kim and H.-Y

    H.-S. Kim and H.-Y. Kee, Crystal structure and mag- netism inα-RuCl 3 : Anab initiostudy, Phys. Rev. B 93, 155143 (2016)

    work page 2016

  46. [46]

    S. M. Winter, Y. Li, H. O. Jeschke, and R. Valent´ ı, Challenges in design of Kitaev materials: Magnetic in- teractions from competing energy scales, Phys. Rev. B 93, 214431 (2016)

    work page 2016

  47. [47]

    S. M. Winter, K. Riedl, P. A. Maksimov, A. L. Cherny- shev, A. Honecker, and R. Valent´ ı, Breakdown of magnons in a strongly spin-orbital coupled magnet, Nat. Commun.8, 1152 (2017)

    work page 2017

  48. [48]

    K. Ran, J. Wang, W. Wang, Z.-Y. Dong, X. Ren, S. Bao, S. Li, Z. Ma, Y. Gan, Y. Zhang, J. T. Park, G. Deng, S. Danilkin, S.-L. Yu, J.-X. Li, and J. Wen, Spin-Wave Excitations Evidencing the Kitaev Interaction in Sin- gle Crystallineα-RuCl 3, Phys. Rev. Lett.118, 107203 (2017)

    work page 2017

  49. [49]

    Janssen, E

    L. Janssen, E. C. Andrade, and M. Vojta, Magnetiza- tion processes of zigzag states on the honeycomb lattice: Identifying spin models forα-RuCl 3 and Na2IrO3, Phys. Rev. B96, 064430 (2017)

    work page 2017

  50. [50]

    Wang, Z.-Y

    W. Wang, Z.-Y. Dong, S.-L. Yu, and J.-X. Li, Theo- retical investigation of magnetic dynamics inα-RuCl 3, Phys. Rev. B96, 115103 (2017)

    work page 2017

  51. [51]

    Cookmeyer and J

    T. Cookmeyer and J. E. Moore, Spin-wave analysis of the low-temperature thermal Hall effect in the candidate Kitaev spin liquidα-RuCl 3, Phys. Rev. B98, 060412(R) (2018)

    work page 2018

  52. [52]

    L. Wu, A. Little, E. E. Aldape, D. Rees, E. Thewalt, P. Lampen-Kelley, A. Banerjee, C. A. Bridges, J.-Q. Yan, D. Boone, S. Patankar, D. Goldhaber-Gordon, D. Man- drus, S. E. Nagler, E. Altman, and J. Orenstein, Field evolution of magnons inα-RuCl 3 by high-resolution po- larized terahertz spectroscopy, Phys. Rev. B98, 094425 (2018). 9

    work page 2018

  53. [53]

    I. O. Ozel, C. A. Belvin, E. Baldini, I. Kimchi, S.-H. Do, K.-Y. Choi, and N. Gedik, Magnetic field-dependent low-energy magnon dynamics inα-RuCl 3, Phys. Rev. B100, 085108 (2019)

    work page 2019

  54. [54]

    Janssen and M

    L. Janssen and M. Vojta, Heisenberg-Kitaev physics in magnetic fields, J. Phys.: Condens. Matter31, 423002 (2019)

    work page 2019

  55. [55]

    E. C. Andrade, L. Janssen, and M. Vojta, Susceptibil- ity anisotropy and its disorder evolution in models for Kitaev materials, Phys. Rev. B102, 115160 (2020)

    work page 2020

  56. [56]

    Kim, H.-S

    C. Kim, H.-S. Kim, and J.-G. Park, Spin-orbital entan- gled state and realization of Kitaev physics in 3d cobalt compounds: a progress report, J. Phys.: Condens. Mat- ter34, 023001 (2022)

    work page 2022

  57. [57]

    Rousochatzakis, N

    I. Rousochatzakis, N. B. Perkins, Q. Luo, and H.-Y. Kee, Beyond Kitaev physics in strong spin-orbit coupled magnets, Rep. Prog. Phys.87, 026502 (2024)

    work page 2024

  58. [58]

    M¨ oller, P

    M. M¨ oller, P. A. Maksimov, S. Jiang, S. R. White, R. Valent´ ı, and A. L. Chernyshev, Rethinkingα-RuCl 3: Parameters, models, and phase diagram, Phys. Rev. B 112, 104403 (2025)

    work page 2025

  59. [59]

    Hentrich, M

    R. Hentrich, M. Roslova, A. Isaeva, T. Doert, W. Brenig, B. B¨ uchner, and C. Hess, Large thermal Hall ef- fect inα-RuCl 3: Evidence for heat transport by Kitaev- Heisenberg paramagnons, Phys. Rev. B99, 085136 (2019)

    work page 2019

  60. [60]

    Vinkler-Aviv and A

    Y. Vinkler-Aviv and A. Rosch, Approximately Quan- tized Thermal Hall Effect of Chiral Liquids Coupled to Phonons, Phys. Rev. X8, 031032 (2018)

    work page 2018

  61. [61]

    M. Ye, G. B. Hal´ asz, L. Savary, and L. Balents, Quanti- zation of the Thermal Hall Conductivity at Small Hall Angles, Phys. Rev. Lett.121, 147201 (2018)

    work page 2018

  62. [62]

    S. Gass, P. M. Cˆ onsoli, V. Kocsis, L. T. Corredor, P. Lampen-Kelley, D. G. Mandrus, S. E. Nagler, L. Janssen, M. Vojta, B. B¨ uchner, and A. U. B. Wolter, Field-induced transitions in the Kitaev materialα- RuCl3 probed by thermal expansion and magnetostric- tion, Phys. Rev. B101, 245158 (2020)

    work page 2020

  63. [63]

    D. A. S. Kaib, S. Biswas, K. Riedl, S. M. Winter, and R. Valent´ ı, Magnetoelastic coupling and effects of uniaxial strain inα-RuCl 3 from first principles, Phys. Rev. B 103, L140402 (2021)

    work page 2021

  64. [64]

    Kocsis, D

    V. Kocsis, D. A. S. Kaib, K. Riedl, S. Gass, P. Lampen- Kelley, D. G. Mandrus, S. E. Nagler, N. P´ erez, K. Nielsch, B. B¨ uchner, A. U. B. Wolter, and R. Valent´ ı, Magnetoelastic coupling anisotropy in the Kitaev mate- rialα-RuCl 3, Phys. Rev. B105, 094410 (2022)

    work page 2022

  65. [65]

    Rigol, T

    M. Rigol, T. Bryant, and R. R. P. Singh, Numerical Linked-Cluster Approach to Quantum Lattice Models, Phys. Rev. Lett.97, 187202 (2006)

    work page 2006

  66. [66]

    Rigol, T

    M. Rigol, T. Bryant, and R. R. P. Singh, Numerical linked-cluster algorithms. I. Spin systems on square, tri- angular, and kagom´ e lattices, Phys. Rev. E75, 061118 (2007)

    work page 2007

  67. [67]

    Oitmaa, C

    J. Oitmaa, C. Hamer, and W. Zheng, Series Expansion Methods for Strongly Interacting Lattice Models (Cam- bridge University Press, 2006)

    work page 2006

  68. [68]

    M. F. Sykes, J. W. Essam, B. R. Heap, and B. J. Hiley, Lattice Constant Systems and Graph Theory, J. Math. Phys.7, 1557 (1966)

    work page 1966

  69. [69]

    R. R. P. Singh and J. Oitmaa, Corrections to Pauling residual entropy and single tetrahedron based approxi- mations for the pyrochlore lattice Ising antiferromagnet, Phys. Rev. B85, 144414 (2012)

    work page 2012

  70. [70]

    Ixert and K

    D. Ixert and K. P. Schmidt, Nonperturbative linked- cluster expansions in long-range ordered quantum sys- tems, Phys. Rev. B94, 195133 (2016)

    work page 2016

  71. [71]

    Khatami and M

    E. Khatami and M. Rigol, Thermodynamics of the an- tiferromagnetic Heisenberg model on the checkerboard lattice, Phys. Rev. B83, 134431 (2011)

    work page 2011

  72. [72]

    Khatami, R

    E. Khatami, R. R. P. Singh, and M. Rigol, Thermody- namics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice, Phys. Rev. B 84, 224411 (2011)

    work page 2011

  73. [73]

    Khatami, J

    E. Khatami, J. S. Helton, and M. Rigol, Numerical study of the thermodynamics of clinoatacamite, Phys. Rev. B85, 064401 (2012)

    work page 2012

  74. [74]

    N. R. Hayre, K. A. Ross, R. Applegate, T. Lin, R. R. P. Singh, B. D. Gaulin, and M. J. P. Gingras, Thermody- namic properties of Yb 2Ti2O7 pyrochlore as a function of temperature and magnetic field: Validation of a quan- tum spin ice exchange Hamiltonian, Phys. Rev. B87, 184423 (2013)

    work page 2013

  75. [75]

    Sch¨ afer, I

    R. Sch¨ afer, I. Hagym´ asi, R. Moessner, and D. J. Luitz, PyrochloreS=1/12 Heisenberg antiferromagnet at finite temperature, Phys. Rev. B102, 054408 (2020)

    work page 2020

  76. [76]

    Mallayya and M

    K. Mallayya and M. Rigol, Numerical linked cluster ex- pansions for quantum quenches in one-dimensional lat- tices, Phys. Rev. E95, 033302 (2017)

    work page 2017

  77. [77]

    Richter, T

    J. Richter, T. Heitmann, and R. Steinigeweg, Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters, Sci- Post Phys.9, 031 (2020)

    work page 2020

  78. [78]

    A. B. Kallin, K. Hyatt, R. R. P. Singh, and R. G. Melko, Entanglement at a Two-Dimensional Quantum Critical Point: A Numerical Linked-Cluster Expansion Study, Phys. Rev. Lett.110, 135702 (2013)

    work page 2013

  79. [79]

    A. B. Kallin, E. M. Stoudenmire, P. Fendley, R. R. P. Singh, and R. G. Melko, Corner contribution to the en- tanglement entropy of anO(3) quantum critical point in 2 + 1 dimensions, J. Stat. Mech.2014, P06009 (2014)

    work page 2014

  80. [80]

    Applegate, N

    R. Applegate, N. R. Hayre, R. R. P. Singh, T. Lin, A. G. R. Day, and M. J. P. Gingras, Vindication of Yb2Ti2O7 as a Model Exchange Quantum Spin Ice, Phys. Rev. Lett.09, 097205 (2012)

    work page 2012

Showing first 80 references.