Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction

T0 review · 3 major / 6 minor · reviewed 2026-07-13 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A third-neighbor Heisenberg term turns the Kitaev spin liquid into magnetically ordered dual pairs at one common critical strength, announced by soft paramagnon modes.

desk verdict First systematic DSF+Raman for the K-J3 model; paramagnon softening and exact T4 duality give a clean common critical |J3| for FM/AFM, though the quoted 0.094 is only approximate. read the letter →

arxiv 2603.24918 v2 pith:ESXEXSBS submitted 2026-03-26 cond-mat.str-el

Chuan Chen , Jiucai Wang This is my paper
classification cond-mat.str-el
keywords Kitaevspinliquidthird-nearest-neighborHeisenbergdynamicalstructurefactorparamagnonmodesfour-sublatticedualityRamanscatteringvisonsMajoranafermions
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

Candidate Kitaev materials often carry a sizable third-nearest-neighbor Heisenberg interaction J3. This paper asks how that term reshapes the dynamical fingerprints of the pure Kitaev spin liquid. Using a self-consistent Majorana parton mean-field theory plus random-phase approximation, the authors show that J3 generates coherent, paramagnon-like collective modes that sit below the usual high-energy Majorana continuum in the spin dynamical structure factor. Those modes soften and condense at a single critical |J3|≈0.094|K|, driving magnetic order. Because of an exact four-sublattice duality that flips the sign of the Kitaev coupling while leaving J3 unchanged, the ferromagnetic and antiferromagnetic Kitaev models order at exactly the same critical strength and the resulting phases form dual pairs (zigzag versus AFM+zigzag, stripe versus FM+stripe). An external magnetic field further softens the same modes, promoting order. Complementary perturbative Raman calculations reveal that the J3 Raman vertex excites both matter Majoranas and visons, producing a sharp four-vison peak plus continua that mirror single- and two-fermion densities of states. The results supply concrete spectral signatures that experiments can use to diagnose the presence and strength of J3 in real materials.

What carries the argument

Self-consistent parton mean-field plus random-phase approximation for the spin dynamical structure factor, together with the exact four-sublattice duality T4 that enforces identical critical |J3| and dual ordered phases for ferromagnetic and antiferromagnetic Kitaev models.

What would settle it

High-resolution inelastic neutron scattering on a candidate material (or large-scale exact diagonalization/DMRG of the pure K-J3 model) that measures the soft-mode gap versus |J3| and finds either a substantially different critical coupling or ordered patterns that violate the predicted T4 duality pairing would falsify the central claim.

Watch

Extended reading notes

Core claim

The third-nearest-neighbor Heisenberg interaction J3 induces coherent paramagnon-like modes that coexist with the Majorana continuum; their gap collapse at a common critical |J3|≈0.094|K| signals magnetic ordering for both signs of the Kitaev coupling K, with the ordered states related by the exact four-sublattice duality that maps (K,J3) to (-K,J3).

Load-bearing premise

The mean-field plus RPA treatment is assumed to locate the magnetic instability correctly even though it overestimates the vison-pair energy by roughly a factor of four, which the authors note already shifts the critical J3 relative to earlier numerical work.

Editorial extensions

If this is right

  • Spin dynamical structure factors of J3-perturbed Kitaev spin liquids should display sharp low-energy paramagnon branches below a largely featureless Majorana continuum.
  • Ferromagnetic and antiferromagnetic Kitaev materials with comparable |J3| must order at the same critical strength, with dual magnetic patterns related by the four-sublattice transformation.
  • An in-plane or c-axis magnetic field will further suppress the paramagnon gaps and accelerate the transition out of the spin-liquid regime.
  • Raman spectra will contain a polarization-dependent A1g channel from the J3 vertex plus a sharp four-vison peak and a continuum that tracks the single-matter-fermion density of states.
  • These spectral templates can be used to extract the relative size of J3 from existing and future inelastic neutron and Raman data on α-RuCl3, iridates, and cobaltates.

Reading between the lines

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

  • If the paramagnon modes remain sharp deep into the disordered regime, field-induced continuum spectra in candidate materials may still be better described as proximate paramagnons than as free Majorana fermions.
  • The two-vison Raman continuum that mimics the single-particle density of states offers a practical route to extract the matter-fermion bandwidth even when local probes cannot create an isolated fermion.
  • Because the duality maps multi-Q and single-Q tendencies into each other, resolving whether the AFM+zigzag and FM+stripe regimes are multi-Q or nearly degenerate single-Q states would simultaneously settle the dual partner on the opposite-K side.
  • Materials in which J3 is known to be large and of fixed sign should show systematically different field-angle dependence of the ordering wave-vector, providing a direct experimental test of the duality-protected phase diagram.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript studies the Kitaev–J3 honeycomb model, focusing on the spin dynamical structure factor (DSF) within a self-consistent Majorana parton mean-field plus RPA framework and on Raman scattering via a perturbative expansion around the exact Kitaev solution. It reports that J3 generates coherent paramagnon-like collective modes coexisting with a high-energy Majorana continuum; these modes soften and condense at a common critical |J3|≈0.094|K| for both ferromagnetic (K<0) and antiferromagnetic (K>0) Kitaev couplings, with the resulting ordered states (zigzag vs AFM+zigzag; stripe vs FM+stripe) related by the exact four-sublattice T4 duality that maps (K,J3)→(−K,J3). An external field further softens preexisting modes, enhancing magnetic order. Perturbative Raman calculations show that the Kitaev-like vertex probes only matter Majoranas, while the J3-like vertex produces distinct two- and four-vison channels, the latter with a sharp peak plus two-fermion continuum and the former with a continuum resembling the single-matter-fermion density of states.

Significance. The work addresses a timely materials-motivated question: third-nearest-neighbor Heisenberg couplings are increasingly recognized as important in α-RuCl3, iridates, and cobaltates, yet their dynamical fingerprints on the Kitaev spin liquid have been less systematically mapped than those of nearest-neighbor Heisenberg or Γ terms. The combination of RPA spin DSF (building on the authors’ prior framework) with exact Kitaev Raman correlators yields concrete, falsifiable spectral signatures—paramagnon modes below the continuum, dual soft-mode patterns, and a two-vison Raman continuum that mimics the single-particle DOS. The exact T4 duality is used cleanly to organize the phase diagram, so the qualitative claim of common critical |J3| and dual ordered pairs is theoretically robust even if the numerical value of |J3|c is approximate. These results should be useful for interpreting inelastic neutron and Raman spectra in candidate materials with sizable J3.

major comments (3)
  1. [Sec. III B, Fig. 4] Sec. III B and Fig. 4 (and the comparison to Ref. [42]): The reported critical value |J3|c≈0.094|K| is extracted entirely from the same mean-field+RPA pipeline that the authors (and Ref. [49]) state overestimates the vison-pair excitation energy by roughly a factor of four. The T4 duality rigorously guarantees that the true critical points of the FM and AFM models coincide and that the ordered states form dual pairs; it does not protect the numerical location of the gap closing inside the biased mean-field landscape. The manuscript should more sharply separate duality-protected statements (common critical |J3|, dual soft-mode momenta) from the approximation-dependent number 0.094, and should discuss how |J3|c would be expected to shift under a corrected vison scale (or under a controlled comparison to ED/DMRG).
  2. [Sec. III C, Figs. 5–8] Sec. III C and Figs. 5–8: Field-induced softening of the same paramagnon modes is used to claim that magnetic fields enhance ordering tendencies, with characteristic scales |h|∼0.2. Because these modes are generated by the identical RPA resummation whose energy scale is known to be inflated, the field scales inherit the same uncontrolled bias. A brief quantitative caveat (or a consistency check against known field-induced transitions in related models) would strengthen the claim that the field “consistently enhances” magnetic order rather than merely shifting an already approximate soft mode.
  3. [Sec. III B, Fig. 1(c), Appendix B] Sec. III B (AFM+zigzag and FM+stripe regimes) and Appendix B: The soft-mode patterns at Γ′/M and Γ/Γ′/M′/M leave open whether the system selects single-Q or multi-Q order; the text defers resolution to variational Monte Carlo “in preparation” [58]. For the phase-diagram claim that anchors the abstract and Fig. 1(c), this is a load-bearing ambiguity. Either a short additional calculation (even on small clusters) or a clearer statement that the present work only diagnoses ordering tendencies, not the final ordered state, is needed so that the dual-pair language is not over-interpreted.
minor comments (6)
  1. [Sec. II] Sec. II, paragraph on duality: typographical error “repsonse” should be “response”.
  2. [Sec. III B] Sec. III B, text after Eq. (22): “related to the mean-field susceptibility in in Eq. (17)” contains a duplicated “in”.
  3. [Fig. 3] Fig. 3 caption and related text: the logarithmic scale ln[1+S(ω,q)] is useful, but a brief note on the absolute intensity scale (or a linear-scale inset for the soft modes) would help experimental comparison.
  4. [Sec. IV B] Sec. IV B: the choice g=0.05 is stated to lie safely below |J3/K|=0.094; it would be helpful to note whether the Raman lineshapes remain qualitatively stable for a few other small g values, or whether any interference between IK and IJ3 was checked beyond the leading-order separation.
  5. [Appendix A] Appendix A: the lists of independent mean-field parameters under h∥a,b,c are clear; a short statement of how self-consistency was monitored (e.g., residual of the constraint equations) would aid reproducibility.
  6. [References] References: Ref. [58] is “Manuscript in preparation (2026)”; if it remains unpublished at acceptance, the multi-Q discussion should stand alone without relying on it for the main claims.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: MF+RPA DSF and perturbative Raman are applied to a new J3 term; common critical |J3| follows from exact T4 duality of the microscopic Hamiltonian, not from a fitted or self-defined construct.

full rationale

The load-bearing claims (J3-induced paramagnon modes that soften at a common |J3|c for both signs of K, dual ordered states related by T4, field-softening of those modes, and the two- versus four-vison Raman continua) are obtained by applying an external parton mean-field + RPA pipeline (Ref. [49], non-overlapping authors) and standard Kitaev exact-solution perturbation theory to the K-J3 Hamiltonian. The T4 map (K,J3) o(-K,J3) is an exact unitary property of the microscopic model (Appendix B), so any approximation that respects the mapping necessarily yields identical critical |J3|; the numerical coincidence observed in the RPA spectra is therefore a consistency check, not a circular prediction. No parameter is fitted to data and then re-presented as a prediction, no uniqueness theorem is imported from the authors’ prior work, and the only self-citation ([58], VMC in preparation) is used only for a non-essential remark on single-Q versus multi-Q preference. The known mean-field overestimate of the vison gap affects quantitative accuracy of |J3|c but does not render the derivation circular. The paper is self-contained against its own equations and external benchmarks.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The calculation rests on standard Majorana parton methods, an established RPA resummation, and the exact T4 duality of the microscopic model. No free parameters are fitted to experimental data; the only numerical inputs are self-consistently determined mean-field amplitudes and a small perturbative ratio g=0.05 chosen safely below the computed critical point. No new particles or forces are postulated.

free parameters (1)
  • perturbative ratio g=λ_J3/λ_K = 0.05
    Set by hand to 0.05 (well below the critical |J3/K|=0.094) to keep the Raman expansion inside the spin-liquid regime; not fitted to data.
assumptions (4)
  • domain assumption Majorana representation of spins with on-average enforcement of the local constraint via Lagrange multipliers
    Standard Kitaev parton construction used throughout Sec. III; exact only for the pure Kitaev model.
  • domain assumption Self-consistent mean-field decoupling of four-Majorana interactions plus RPA resummation of residual interactions
    Framework of Ref. [49] adopted in Sec. III; known to overestimate vison-pair energy by ~4.
  • standard math Four-sublattice unitary T4 maps (K,J3) o(-K,J3) exactly
    Exact microscopic duality (Appendix B) used to relate FM and AFM critical points and ordered states.
  • domain assumption Loudon-Fleury Raman operator and leading-order multi-particle truncation for vison channels
    Standard approximation for magnetic Raman scattering; higher-order γ0 correlators discarded as density-of-states suppressed (Sec. IV).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction." pith.science (2026). https://pith.science/paper/ESXEXSBS

@misc{pith2026260324918,
  author       = {Pith},
  title        = {Pith review of: Dynamical Response of the Kitaev Spin Liquid under Third-Nearest-Neighbor Heisenberg Interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ESXEXSBS}},
  note         = {Machine review of arXiv:2603.24918}
}
abstract

Motivated by growing evidence for the significance of the third-nearest-neighbor Heisenberg ($J_3$) interaction in candidate Kitaev materials, we investigate the dynamical properties of the Kitaev spin liquid (KSL) under a $J_3$ perturbation, focusing on its spin dynamical structure factor (DSF) and Raman scattering. Within a self-consistent parton mean-field plus random-phase approximation framework, we find that $J_3$ induces coherent, paramagnon-like collective modes that coexist with a high-energy Majorana continuum in the spin DSF. The softening of these modes with increasing $|J_3|$ signals a quantum phase transition to magnetic order. Remarkably, magnetic ordering sets in at a common critical $J_3$ for both ferromagnetic ($K<0$) and antiferromagnetic ($K>0$) Kitaev models, with the resulting ordered states forming exact dual pairs under a four-sublattice duality transformation that maps $(K,J_3) \rightarrow (-K,J_3)$. An external magnetic field further softens the preexisting paramagnon modes, thereby enhancing magnetic order. Perturbative Raman calculations show that while the Kitaev-like Raman vertex probes only itinerant matter Majorana fermions, the response from the $J_3$-like vertex features both matter Majoranas and visons. Four-vison excitations produce a sharp peak accompanied by a two-fermion continuum, whereas two-vison excitations yield a continuum closely resembling the single-matter-fermion density of states. These results provide a unified perspective on the dynamical signatures of $J_3$-perturbed KSL and are helpful for interpreting experimental spectra in candidate Kitaev materials with sizable $J_3$ interactions.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Evidence for Deconfined Magnetic Order in the Kitaev-$J_3$ Model

    cond-mat.str-el 2026-07 unverdicted novelty 6.0 of 10

    The Kitaev-J3 model hosts deconfined magnetic phases in which zigzag or antiferromagnetic order coexists with remnant Z2 topological structure inherited from the Kitaev spin liquid through vison-pair condensation.

Reference graph

Works this paper leans on

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

  1. [42]

    Singh, S

    Y. Singh, S. Manni, J. Reuther, T. Berlijn, R. Thomale, W. Ku, S. Trebst, and P. Gegenwart, Relevance of the heisenberg-kitaev model for the honeycomb lattice iri- dates A2IrO3, Phys. Rev. Lett.108, 127203 (2012)

    2012

  2. [49]

    A. L. Sanders, R. A. Mole, J. Liu, A. J. Brown, D. Yu, C. D. Ling, and S. Rachel, Dominant Kitaev inter- actions in the honeycomb materialsNa 3Co2SbO6 and Na2Co2TeO6, Phys. Rev. B106, 014413 (2022)

    2022

  3. [58]

    Y.-Z. You, I. Kimchi, and A. Vishwanath, Doping a spin- orbit mott insulator: Topological superconductivity from the kitaev-heisenberg model and possible application to (Na2/Li2)IrO3, Phys. Rev. B86, 085145 (2012)

    2012

  4. [1]

    ω= 4|K|, and terminates atω= 12|K|

    (b) Two-vison configuration generated by σz 5 σz 8 andσ z 7 σz 6. ω= 4|K|, and terminates atω= 12|K|. Fig. 10(b) shows the total intensity versus polarization angle, which is independent of polarization, as expected. UnlikeR K,R J3 creates vison excitations. Depending on the orientation of⟨i, j⟩3 and the spin components of the bilinear terms in Eq. (23b),...

  5. [2]

    Therefore F 4v 1,z(t) = (2δz ·ϵ in)2(2δz ·ϵ out)2 C 4v 1,z(t),(34a) C 4v 1,z(t) =⟨Ω|e iHK tσz 1σz 4e−iHK tσz 1σz 4|Ω⟩.(34b) Utilizing the Majorana fermion representation, the cor- relator can be written as C 4v 1,z(t) =⟨Ψ a 0|eiH a 0 te−i[H a 0 +V 4v]t|Ψa 0⟩.(35) Here the local perturbationV 4v, corresponding to four additional visons, is given by V 4v =−...

    2025

  6. [3]

    P. A. Lee, N. Nagaosa, and X. G. Wen, Doping a mott in- sulator: Physics of high-temperature superconductivity, Rev. Mod. Phys.78, 17 (2006)

    2006

  7. [4]

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

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

    2010

  8. [5]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a re- view, Rep. Prog. Phys.80, 016502 (2017)

    2017

Show all 67 references
  1. [6]

    Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states, Rev. Mod. Phys.89, 025003 (2017)

    2017

  2. [7]

    Broholm, R

    C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Quantum spin liquids, Science367, 10.1126/science.aay0668 (2020)

    2020 doi

  3. [8]

    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)

    2006

  4. [9]

    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)

    2009

  5. [10]

    Hermanns, I

    M. Hermanns, I. Kimchi, and J. Knolle, Physics of the ki- taev model: Fractionalization, dynamic correlations, and material connections, Annu. Rev. Condens. Matter Phys. 9, 17 (2018)

    2018

  6. [11]

    Knolle and R

    J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys.10, 451 (2019)

    2019

  7. [12]

    Takagi, T

    H. Takagi, T. Takayama, G. Jackeli, G. Khaliullin, and S. E. Nagler, Concept and realization of kitaev quantum spin liquids, Nature Reviews Physics1, 264 (2019)

    2019

  8. [13]

    Trebst and C

    S. Trebst and C. Hickey, Kitaev materials, Physics Re- ports950, 1 (2022)

    2022

  9. [14]

    Rousochatzakis, N

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

    2024

  10. [15]

    Matsuda, T

    Y. Matsuda, T. Shibauchi, and H.-Y. Kee, Kitaev quan- tum spin liquids, Rev. Mod. Phys.97, 045003 (2025)

    2025

  11. [16]

    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. Moess- ner, D. A. Tennant, D. G. Mandrus, and S. E. Nagler, Proximate kitaev quantum spin liquid behaviour in a honey...

    2016

  12. [17]

    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)

    2017

  13. [18]

    Banerjee, P

    A. Banerjee, P. Lampen-Kelley, J. Knolle, C. Balz, A. A. Aczel, B. Winn, Y. Liu, D. Pajerowski, J. Yan, C. A. Bridges, A. T. Savici, B. C. Chakoumakos, M. D. Lums- den, D. A. Tennant, R. Moessner, D. G. Mandrus, and S. E. Nagler, Excitations in the field-induced quantum 16 spi...

    2018

  14. [19]

    Kasahara, T

    Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Mo- tome, T. Shibauchi, and Y. Matsuda, Majorana quanti- zation and half-integer thermal quantum hall effect in a kitaev spin liquid, Nature559, 227 (2018), 1805.05022

    2018 arXiv

  15. [20]

    Kurita, H

    T.Yokoi, S.Ma, Y.Kasahara, S.Kasahara, T.Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, C. Hickey, S. Trebst, and Y. Matsuda, Half-integer quantized anomalous thermal hall effect in the kitaev material can- didateα-RuCl 3, Science373, 568 (2021)

    2021

  16. [21]

    Czajka, T

    P. Czajka, T. Gao, M. Hirschberger, P. Lampen-Kelley, A. Banerjee, J. Yan, D. G. Mandrus, S. E. Nagler, and N. P. Ong, Oscillations of the thermal conductivity in the spin-liquid state ofα-RuCl3, Nat. Phys.17, 915 (2021)

    2021

  17. [22]

    Czajka, T

    P. Czajka, T. Gao, M. Hirschberger, P. Lampen-Kelley, A. Banerjee, N. Quirk, D. G. Mandrus, S. E. Nagler, and N. P. Ong, Planar thermal hall effect of topological bosons in the kitaev magnetα-RuCl 3, Nat. Mater.22, 36 (2023)

    2023

  18. [23]

    Lefrançois, G

    E. Lefrançois, G. Grissonnanche, J. Baglo, P. Lampen- Kelley, J.-Q. Yan, C. Balz, D. Mandrus, S. E. Nagler, S. Kim, Y.-J. Kim, N. Doiron-Leyraud, and L. Taillefer, Evidence of a phonon hall effect in the kitaev spin liquid candidateα-RuCl 3, Phys. Rev. X12, 021025 (2022)

    2022

  19. [24]

    Lefrançois, J

    E. Lefrançois, J. Baglo, Q. Barthélemy, S. Kim, Y.-J. Kim, and L. Taillefer, Oscillations in the magnetothermal conductivity ofα-RuCl 3: Evidence of transition anoma- lies, Phys. Rev. B107, 064408 (2023)

    2023

  20. [25]

    I. S. Villadiego, Pseudoscalar U(1) spin liquids inα- RuCl3, Phys. Rev. B104, 195149 (2021)

    2021

  21. [26]

    L. E. Chern, E. Z. Zhang, and Y. B. Kim, Sign structure of thermal hall conductivity and topological magnons for in-plane field polarized kitaev magnets, Phys. Rev. Lett. 126, 147201 (2021)

    2021

  22. [27]

    Chaloupka, G

    J. Chaloupka, G. Jackeli, and G. Khaliullin, Kitaev- heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3, Phys. Rev. Lett.105, 027204 (2010)

    2010

  23. [28]

    Chaloupka, G

    J. Chaloupka, G. Jackeli, and G. Khaliullin, Zigzag mag- neticorderintheiridiumoxideNa 2IrO3,Phys.Rev.Lett. 110, 097204 (2013)

    2013

  24. [29]

    Kimchi and Y.-Z

    I. Kimchi and Y.-Z. You, Kitaev-heisenberg-J2-J3 model for the iridates A2IrO3, Phys. Rev. B84, 180407 (2011)

    2011

  25. [30]

    Knolle, S

    J. Knolle, S. Bhattacharjee, and R. Moessner, Dy- namics of a quantum spin liquid beyond integrability: The kitaev-heisenberg-γmodel in an augmented parton mean-field theory, Phys. Rev. B97, 134432 (2018)

    2018

  26. [31]

    J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Generic spin model for the honeycomb iridates beyond the kitaev limit, Phys. Rev. Lett.112, 077204 (2014)

    2014

  27. [32]

    J. S. Gordon, A. Catuneanu, E. S. Sørensen, and H.-Y. Kee, Theory of the field-revealed kitaev spin liquid, Nat. Commun.10, 2470 (2019)

    2019

  28. [33]

    E. S. Sørensen, A. Catuneanu, J. S. Gordon, and H.-Y. Kee, Heart of entanglement: Chiral, nematic, and incom- mensurate phases in the kitaev-gamma ladder in a field, Phys. Rev. X11, 011013 (2021)

    2021

  29. [34]

    Kawashima, and Y

    H.-Y.Lee, R.Kaneko, L.E.Chern, T.Okubo, Y.Yamaji, N. Kawashima, and Y. B. Kim, Magnetic field induced quantum phases in a tensor network study of kitaev mag- nets, Nat. Commun.11, 1639 (2020)

    2020

  30. [35]

    J. Wang, B. Normand, and Z.-X. Liu, One proximate kitaev spin liquid in the K-J-Γmodel on the honeycomb lattice, Phys. Rev. Lett.123, 197201 (2019)

    2019

  31. [36]

    J. Wang, B. Normand, and Z.-X. Liu, Multinode quan- tum spin liquids in extended kitaev honeycomb models, npj Quantum Mater.9, 1 (2024)

    2024

  32. [37]

    Zhang, G

    S.-S. Zhang, G. B. Halász, W. Zhu, and C. D. Batista, Variationalstudyofthekitaev-heisenberg-gammamodel, Phys. Rev. B104, 014411 (2021)

    2021

  33. [38]

    Chen and I

    C. Chen and I. S. Villadiego, Anyon polarons as a window into the competing phases of the Kitaev- Gamma-Gamma’ model, arXiv [cond-mat.str-el] (2025), arXiv:2508.21129

    2025 arXiv

  34. [39]

    P. A. Maksimov and A. L. Chernyshev, Rethinkingα- RuCl3, Phys. Rev. Res.2, 033011 (2020)

    2020

  35. [40]

    Möller, P

    M. Möller, P. A. Maksimov, S. Jiang, S. R. White, R. Valenti, and A. L. Chernyshev, The saga ofα-RuCl3: Parameters, models, and phase diagrams, arXiv [cond- mat.str-el] (2025), arXiv:2502.08698

    2025 arXiv

  36. [41]

    S. K. Choi, R. Coldea, A. N. Kolmogorov, T. Lancaster, I. I. Mazin, S. J. Blundell, P. G. Radaelli, Y. Singh, P. Gegenwart, K. R. Choi, S.-W. Cheong, P. J. Baker, C. Stock, and J. Taylor, Spin waves and revised crystal structureofhoneycombiridateNa 2IrO3,Phys.Rev.Lett. 108, 12...

    2012

  37. [43]

    C. Kim, J. Jeong, G. Lin, P. Park, T. Masuda, S. Asai, S. Itoh, H.-S. Kim, H. Zhou, J. Ma, and J.-G. Park, An- tiferromagnetic Kitaev interaction in Jef f = 1/2 cobalt honeycomb materials Na3Co2SbO6 and Na2Co2TeO6, J. Phys.: Condens. Matter34, 045802 (2021)

    2021

  38. [44]

    B. H. Kim, S. Sota, T. Shirakawa, S. Yunoki, and Y.-W. Son, Proximate kitaev system for an intermediate mag- netic phase in in-plane magnetic fields, Phys. Rev. B. 102, 140402 (2020)

    2020

  39. [45]

    G. Lin, J. Jeong, C. Kim, Y. Wang, Q. Huang, T. Ma- suda, S. Asai, S. Itoh, G. Günther, M. Russina, Z. Lu, J. Sheng, L. Wang, J. Wang, G. Wang, Q. Ren, C. Xi, W. Tong, L. Ling, Z. Liu, L. Wu, J. Mei, Z. Qu, H. Zhou, X. Wang, J.-G. Park, Y. Wan, and J. Ma, Field-induced quantum...

    2021

  40. [46]

    W. Yao, K. Iida, K. Kamazawa, and Y. Li, Excitations in the ordered and paramagnetic states of honeycomb mag- net Na2Co2TeO6, Phys. Rev. Lett.129, 147202 (2022)

    2022

  41. [47]

    M.Songvilay, J.Robert, S.Petit, J.A.Rodriguez-Rivera, W. D. Ratcliff, F. Damay, V. Balédent, M. Jiménez-Ruiz, P. Lejay, E. Pachoud, A. Hadj-Azzem, V. Simonet, and C. Stock, Kitaev interactions in the Co honeycomb anti- ferromagnetsNa 3Co2SbO6 andNa 2Co2TeO6, Phys. Rev. B102, 2...

    2020

  42. [48]

    A. M. Samarakoon, Q. Chen, H. Zhou, and V. O. Garlea, Static and dynamic magnetic properties of honeycomb lattice antiferromagnetsNa 2M2TeO6,M= Coand Ni, Phys. Rev. B104, 184415 (2021)

    2021

  43. [50]

    G. Lin, M. Shu, Q. Zhao, G. Li, Y. Ma, J. Jiao, Y. Li, G. Duan, Q. Huang, J. Sheng,et al., Evidence for field induced quantum spin liquid behavior in a spin- 17 1/2 honeycomb magnet, The Innovation Materials2, 10.59717/j.xinn-mater.2024.100082 (2024)

    2024 doi

  44. [51]

    P. Rao, R. Moessner, and J. Knolle, Dynamical response theory of interacting majorana fermions and its appli- cation to generic kitaev quantum spin liquids in a field, Phys. Rev. B.112, 024440 (2025)

    2025

  45. [52]

    Knolle, G.-W

    J. Knolle, G.-W. Chern, D. L. Kovrizhin, R. Moessner, and N. B. Perkins, Raman scattering signatures of kitaev spin liquids in A2IrO3 iridates with A=Na or Li, Phys. Rev. Lett.113, 187201 (2014)

    2014

  46. [53]

    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)

    2016

  47. [54]

    Zou and Y.-C

    L. Zou and Y.-C. He, Field-induced QCD3-chern-simons quantum criticalities in kitaev materials, Phys. Rev. Res. 2, 013072 (2020)

    2020

  48. [55]

    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)

    2014

  49. [56]

    Knolle, D

    J. Knolle, D. L. Kovrizhin, J. T. Chalker, and R. Moess- ner, Dynamics of fractionalization in quantum spin liq- uids, Phys. Rev. B.92, 115127 (2015)

    2015

  50. [57]

    Wen, Quantum orders and symmetric spin liquids, Phys

    X.-G. Wen, Quantum orders and symmetric spin liquids, Phys. Rev. B.65, 165113 (2002)

    2002

  51. [59]

    Auerbach,Interacting electrons and quantum mag- netism,1sted.,GraduateTextsinContemporaryPhysics (Springer, New York, NY, 1998)

    A. Auerbach,Interacting electrons and quantum mag- netism,1sted.,GraduateTextsinContemporaryPhysics (Springer, New York, NY, 1998)

    1998

  52. [60]

    Wang and C

    J. Wang and C. Chen, Manuscript in preparation (2026)

    2026

  53. [61]

    T. P. Devereaux and R. Hackl, Inelastic light scatter- ing from correlated electrons, Rev. Mod. Phys.79, 175 (2007)

    2007

  54. [62]

    Cépas, J

    O. Cépas, J. O. Haerter, and C. Lhuillier, Detection of weak emergent broken-symmetries of the kagome anti- ferromagnet by raman spectroscopy, Phys. Rev. B.77, 172406 (2008)

    2008

  55. [63]

    P. A. Fleury and R. Loudon, Scattering of light by one- and two-magnon excitations, Phys. Rev.166, 514 (1968)

    1968

  56. [64]

    Consequently, terms involving higher-orderγ0 correlators mainly contribute to a broad continuum and are strongly suppressed at low energies [50]

    The multi-γ0 correlation function scales with a higher power of the density of states of the matter fermions. Consequently, terms involving higher-orderγ0 correlators mainly contribute to a broad continuum and are strongly suppressed at low energies [50]

  57. [65]

    In calculating the spin DSF of the Kitaev model, this type of approximation has been shown to reproduce the exact results accurately [50, 54]

  58. [66]

    L. M. Robledo, Sign of the overlap of hartree-fock- bogoliubov wave functions, Phys. Rev. C79, 021302 (2009)

    2009

  59. [67]

    Ring and P

    P. Ring and P. Schuck,The nuclear many-body problem, Theoretical and Mathematical Physics (Springer, Berlin, Germany, 2004)

    2004

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.