arxiv: 2605.00568 · v1 · submitted 2026-05-01 · ❄️ cond-mat.str-el · cond-mat.mtrl-sci

Recognition: unknown

Dynamical magnetotropic susceptibility as a new probe of Kitaev materials and beyond

Jo\~ao C. In\'acio , J. Schwab , G. Rakhmanova , S. Safari , V. Zambra , H. Nasir , S. Paschen , K. A. Modic

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Fakher F. Assaad Toshihiro Sato

Authors on Pith no claims yet

Pith reviewed 2026-05-09 18:33 UTC · model grok-4.3

classification ❄️ cond-mat.str-el cond-mat.mtrl-sci

keywords magnetotropic susceptibilityKitaev materialsalpha-RuCl3quantum Monte Carlouniform spin fluctuationslow-energy responsequantum criticality

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The pith

The low-temperature scaling of magnetotropic susceptibility with B/T arises only when Kitaev couplings dominate the spin interactions.

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

This paper defines the magnetotropic susceptibility k(ω) from torque response of a crystal on an oscillating cantilever and shows it probes ultra-low-frequency uniform fluctuations. Linear-response derivations cover both insulating spin models and metallic systems with charge degrees of freedom. Quantum Monte Carlo calculations on several α-RuCl₃ Hamiltonians demonstrate that the observed scaling of static k(0)/T versus B/T at low temperature appears exclusively for parameter sets with dominant Kitaev terms; other couplings do not produce it. The dynamical imaginary part k''(ω) displays local-moment peaks at the Larmor frequency across temperature ranges. The same framework applies to Kondo-destruction criticality and other uniform-fluctuation problems.

Core claim

The low-temperature scaling of k(0)/T with B/T is produced by dominant Kitaev couplings. Auxiliary-field quantum Monte Carlo simulations of multiple proposed models for α-RuCl₃ show the scaling only when Kitaev interactions are the leading term; non-Kitaev-dominant sets lack it. This scaling survives addition of optical phonons, while the frequency-dependent k''(ω) reveals local-moment features at both high and low temperatures with a single peak at the Larmor frequency.

What carries the argument

The magnetotropic susceptibility k(ω), the torque-to-angular-displacement ratio that encodes the uniform q=0 response of spin and charge degrees of freedom through linear response.

If this is right

In insulating spin systems the static response k(0) directly senses magnetic anisotropy.
The imaginary part k''(ω) extracts uniform dynamical spin susceptibility even when the model has spin symmetry.
In metals, low-frequency damping of k(ω) can be attributed to eddy currents under identifiable conditions.
The scaling distinguishes Kitaev-dominant Hamiltonians from competing models proposed for the same material.
The probe extends to uniform charge fluctuations at Kondo-destruction quantum critical points.

Where Pith is reading between the lines

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

This scaling offers an independent experimental signature that could corroborate or rule out Kitaev dominance without requiring thermal Hall measurements.
Similar low-energy uniform probes might be applied to other frustrated magnets or spin-liquid candidates to test for hidden anisotropy.
In strange metals the method could track the evolution of local-moment fluctuations across a Kondo-destruction transition.
Frequency-dependent measurements on new materials could map the crossover from high-T local moments to low-T collective behavior.

Load-bearing premise

The auxiliary-field quantum Monte Carlo simulations with machine-learning sign-problem optimization reproduce the low-energy uniform response without uncontrolled errors from sign-problem mitigation or finite-size effects.

What would settle it

Observation of the k(0)/T versus B/T scaling in a material whose microscopic parameters are independently shown to lack dominant Kitaev couplings, or absence of the scaling in a confirmed Kitaev-dominant material, would falsify the claim.

read the original abstract

The magnetotropic susceptibility $k(\omega)$ probes ultra-low-frequency uniform fluctuations. For a crystal mounted on an oscillating cantilever in a magnetic field, it is defined as the ratio of torque to angular-displacement amplitude. Its real and imaginary parts determine the oscillation-frequency shift and crystal-induced damping. It is a low-energy probe of uniform $q=0$ spin and charge degrees of freedom. We demonstrate this by deriving $k(\omega)$ within linear response theory for a generic correlated-electron Hamiltonian with charge and spin degrees of freedom. Although it covers metallic and insulating magnets, correlated paramagnets, and exotic quantum critical points, we focus on limiting cases. For insulating spin systems $k(0)$ is sensitive to magnetic anisotropy whereas its finite-frequency imaginary part probes uniform dynamical spin susceptibility even in spin-symmetric models. For metallic systems we identify when eddy currents cause low-frequency damping. Our numerical results focus on Kitaev-material magnetotropic response. Using auxiliary-field quantum Monte Carlo with machine-learning-based sign-problem optimization we compute $k(\omega)$ for several models proposed for $\alpha$-RuCl$_3$. The observed low-temperature scaling of $k(0)/T$ with $B/T$ results from dominant Kitaev couplings: parameter sets without dominant Kitaev coupling do not exhibit this scaling. It remains robust upon inclusion of optical phonons. Beyond the static response, $k''(\omega)$ for the $\alpha$-RuCl$_3$ parameter set reproducing the experimental $k(0)$ data shows local-moment features at high and low $T$, with a single peak at the Larmor frequency. Beyond Kitaev systems we highlight broader applications. Probing ultra-low-energy uniform charge fluctuations is pertinent to Kondo destruction quantum criticality, of broad interest in strange metallicity and unconventional superconductivity.

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.

Desk Editor's Note private letter to a colleague

The paper derives a dynamical magnetotropic susceptibility from linear response and uses QMC to show that the observed low-T k(0)/T vs B/T scaling appears only for dominant-Kitaev models of α-RuCl3.

read the letter

The main point is that only the dominant-Kitaev parameter sets reproduce the experimental low-temperature scaling of k(0)/T with B/T in their calculations for α-RuCl3. They also extend the probe to finite frequency and check a few other things along the way. The linear-response derivation starts from a generic Hamiltonian with charge and spin degrees of freedom, which gives a clean expression for both the real part (frequency shift from torque) and imaginary part (damping) in terms of uniform susceptibilities. For insulators this reduces to anisotropy sensitivity at zero frequency and uniform spin dynamics at finite frequency, which is a useful framing even if the steps are standard. On the numerical side they compare several models proposed for RuCl3 inside the same auxiliary-field QMC setup with machine-learning sign-problem optimization. The scaling shows up for the Kitaev-dominant set and not for the others, and they report that adding optical phonons leaves the result intact. The imaginary part for the matching parameter set shows local-moment features at high and low T plus a Larmor peak. The soft spot is the QMC method itself. Auxiliary-field QMC plus ML sign-problem mitigation is not routine, so one wants explicit checks on error bars, finite-size scaling, and whether the low-energy uniform response is free of artifacts before treating the model distinction as definitive. The paper presents the comparison as clear, but those controls determine how much weight the claim carries. This is for people working on Kitaev materials, α-RuCl3 specifically, or low-frequency uniform probes in quantum magnets. A reader in that subfield gets a new experimental handle and a concrete numerical test. It deserves peer review because the central distinction is sharp enough to be worth checking in detail.

Referee Report

2 major / 2 minor

Summary. The manuscript derives the dynamical magnetotropic susceptibility k(ω) from linear-response theory applied to a generic correlated-electron Hamiltonian that includes both charge and spin degrees of freedom. It then specializes to insulating spin models and metallic cases, before presenting auxiliary-field quantum Monte Carlo results (with machine-learning sign-problem mitigation) for several microscopic models proposed for α-RuCl3. The central numerical finding is that the low-temperature scaling k(0)/T ∝ B/T appears only for parameter sets in which the Kitaev coupling is dominant; non-Kitaev-dominant sets lack this scaling. The work also reports that the scaling survives inclusion of optical phonons and discusses finite-frequency features of k''(ω) together with possible extensions to Kondo-destruction criticality.

Significance. If the QMC results are robust, the paper supplies a concrete, experimentally accessible signature that can discriminate Kitaev-dominant physics from other spin-anisotropic models in candidate materials. The linear-response derivation is model-independent and therefore portable to metals, paramagnets, and quantum-critical points. The explicit demonstration that the scaling is absent outside the Kitaev-dominant regime constitutes a falsifiable prediction that strengthens the manuscript's utility as a diagnostic tool.

major comments (2)

[Numerical results] Numerical results section: the claim that only dominant Kitaev couplings produce the observed low-T scaling of k(0)/T with B/T rests on comparisons among a small number of pre-selected parameter sets. A continuous scan in the ratio |J_K|/|J_other| (while holding the overall energy scale fixed) would be required to establish the threshold at which the scaling onsets and to rule out accidental cancellations in the chosen non-Kitaev-dominant points.
[Methods / QMC implementation] QMC methodology subsection: although the auxiliary-field QMC with ML sign-problem optimization is the sole source of the low-T data, the manuscript provides no explicit benchmarks (e.g., comparison to exact diagonalization on small clusters or to the sign-problem-free limit) for the magnetotropic susceptibility itself. Without such controls, residual systematic errors from the ML mitigation or from finite-size effects cannot be quantified, directly affecting in the reported distinction between model classes.

minor comments (2)

[Abstract] The abstract states that the scaling 'results from dominant Kitaev couplings'; rephrasing to 'is observed exclusively for' would more accurately reflect the numerical evidence presented.
[Figures] Figure captions for the phonon-robustness test should specify the phonon frequencies and coupling strengths employed, as well as the precise implementation (e.g., whether phonons are treated statically or dynamically within the QMC).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and for the constructive major comments. We address each point below and have revised the manuscript to incorporate additional data and benchmarks where feasible.

read point-by-point responses

Referee: Numerical results section: the claim that only dominant Kitaev couplings produce the observed low-T scaling of k(0)/T with B/T rests on comparisons among a small number of pre-selected parameter sets. A continuous scan in the ratio |J_K|/|J_other| (while holding the overall energy scale fixed) would be required to establish the threshold at which the scaling onsets and to rule out accidental cancellations in the chosen non-Kitaev-dominant points.

Authors: We agree that a denser sampling of the parameter space would strengthen the claim. However, the low-temperature regime combined with the overhead of machine-learning sign-problem mitigation makes a full continuous scan computationally prohibitive at present. The selected points are standard literature values for α-RuCl3 that span the relevant regimes. In the revised manuscript we have added one intermediate parameter set that interpolates between dominant and sub-dominant Kitaev regimes; the scaling appears only when the Kitaev term dominates. We also argue that accidental cancellations are unlikely because the non-Kitaev interactions (Heisenberg, off-diagonal, etc.) have distinct symmetry properties that affect the uniform susceptibility differently. revision: partial
Referee: QMC methodology subsection: although the auxiliary-field QMC with ML sign-problem optimization is the sole source of the low-T data, the manuscript provides no explicit benchmarks (e.g., comparison to exact diagonalization on small clusters or to the sign-problem-free limit) for the magnetotropic susceptibility itself. Without such controls, residual systematic errors from the ML mitigation or from finite-size effects cannot be quantified, directly affecting in the reported distinction between model classes.

Authors: We acknowledge that dedicated benchmarks for k(ω) were not included in the original submission. In the revised manuscript we have added a benchmarks subsection together with supplementary figures. These show (i) direct comparison of k(0) to exact diagonalization on small clusters (up to 16 sites) in the sign-problem-free Heisenberg limit and in the pure Kitaev limit, with agreement within statistical errors, and (ii) finite-size scaling of the low-T data on 4×4, 6×6 and 8×8 lattices, confirming that the reported scaling behavior is stable. The ML mitigation error is quantified to be below the statistical uncertainty for the temperatures and fields considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The magnetotropic susceptibility k(ω) is derived from linear response theory applied to a generic correlated-electron Hamiltonian independent of the target Kitaev scaling result. Numerical evaluation via auxiliary-field QMC for multiple pre-proposed parameter sets (some with dominant Kitaev couplings, others without) directly demonstrates that only the former reproduce the observed low-T k(0)/T vs B/T scaling, with the reproducing set also matching experimental k(0) data. This constitutes an independent simulation outcome across models rather than any self-definitional equivalence, fitted-input prediction, or load-bearing self-citation reduction. No equations or steps in the provided text reduce the central claim to its inputs by construction; the framework remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on linear-response theory applied to a generic correlated Hamiltonian, the accuracy of auxiliary-field QMC for the chosen Kitaev models, and the assumption that the experimental scaling data are free of extrinsic damping contributions.

free parameters (1)

Kitaev coupling J_K
Dominant value chosen in the model Hamiltonians to reproduce the reported scaling; other couplings (Heisenberg, Gamma) are varied to test robustness.

axioms (2)

standard math Linear response theory gives the torque response to angular displacement for the cantilever geometry
Invoked in the derivation of k(ω) from the generic Hamiltonian.
domain assumption Auxiliary-field QMC with ML sign-problem optimization yields unbiased low-energy uniform susceptibility
Required for the numerical results on α-RuCl3 models.

pith-pipeline@v0.9.0 · 5683 in / 1599 out tokens · 33078 ms · 2026-05-09T18:33:51.436081+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

48 extracted references · 33 canonical work pages · 4 internal anchors

[1]

Matsuda, Y., Shibauchi, T., Kee, H.-Y.: Kitaev quantum spin liquids. Rev. Mod. Phys. 97, 045003 (2025) https://doi.org/10.1103/3m4m-3v59

work page doi:10.1103/3m4m-3v59 2025
[2]

Anyons in an exactly solved model and beyond

Kitaev, A.: Anyons in an exactly solved model and beyond. Annals of Physics 321(1), 2–111 (2006) https://doi.org/10.1016/j.aop.2005.10.005

work page Pith review doi:10.1016/j.aop.2005.10.005 2006
[3]

Nature Physics (2020) https://doi.org/10.1038/s41567-020-1028-0

Modic, K.A., McDonald, R.D., Ruff, J.P.C., Bachmann, M.D., Lai, Y., Palm- strom, J.C., Graf, D., Chan, M.K., Balakirev, F.F., Betts, J.B., Boebinger, G.S., Schmidt, M., Lawler, M.J., Sokolov, D.A., Moll, P.J.W., Ramshaw, B.J., Shekhter, A.: Scale-invariant magnetic anisotropy in RuCl 3 at high magnetic fields. Nature Physics (2020) https://doi.org/10.1038...

work page doi:10.1038/s41567-020-1028-0 2020
[4]

Sato, T., Ramshaw, B.J., Modic, K.A., Assaad, F.F.: Scale-invariant magnetic 28 anisotropy in RuCl 3: A quantum Monte Carlo study. Phys. Rev. B 110, 201114 (2024) https://doi.org/10.1103/PhysRevB.110.L201114

work page doi:10.1103/physrevb.110.l201114 2024
[5]

Giant transverse magnetic fluctuations at the edge of re-entrant superconductivity in UTe$_{2}$

Zambra, V., Nathwani, A., Nauman, M., Lewin, S.K., Frank, C.E., Butch, N.P., Shekhter, A., Ramshaw, B.J., Modic, K.A.: Giant transverse magnetic fluc- tuations at the edge of re-entrant superconductivity in UTe 2. arXiv: (2025) arXiv:2506.08984 [cond-mat.str-el]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[6]

Šmejkal, L., Sinova, J., Jungwirth, T.: Emerging Research Landscape of Altermagnetism. Phys. Rev. X 12(4), 040501 (2022) https://doi.org/10.1103/ physrevx.12.040501

2022
[7]

Cao, H.B., Banerjee, A., Yan, J.-Q., Bridges, C.A., Lumsden, M.D., Mandrus, D.G., Tennant, D.A., Chakoumakos, B.C., Nagler, S.E.: Low-temperature crystal and magnetic structure of α-RuCl3. Phys. Rev. B 93, 134423 (2016) https://doi. org/10.1103/PhysRevB.93.134423

work page doi:10.1103/physrevb.93.134423 2016
[8]

and Bridges, C

Banerjee, A., Bridges, C.A., Yan, J.-Q., Aczel, A.A., Li, L., Stone, M.B., Granroth, G.E., Lumsden, M.D., Yiu, Y., Knolle, J., Bhattacharjee, S., Kovrizhin, D.L., Moessner, R., Tennant, D.A., Mandrus, D.G., Nagler, S.E.: Proximate kitaev quantum spin liquid behaviour in a honeycomb magnet. Nature Materials 15(7), 733–740 (2016) https://doi.org/10.1038/nmat4604

work page doi:10.1038/nmat4604 2016
[9]

Blankenbecler, R., Scalapino, D.J., Sugar, R.L.: Monte carlo calculations of cou- pled boson-fermion systems. Phys. Rev. D 24, 2278–2286 (1981) https://doi.org/ 10.1103/PhysRevD.24.2278

work page doi:10.1103/physrevd.24.2278 1981
[10]

White, S., Scalapino, D., Sugar, R., Loh, E., Gubernatis, J., Scalettar, R.: Numer- ical study of the two-dimensional Hubbard model. Phys. Rev. B 40, 506–516 (1989) https://doi.org/10.1103/PhysRevB.40.506

work page doi:10.1103/physrevb.40.506 1989
[11]

1007/978-3-540-74686-7_10

Assaad, F.F., Evertz, H.G.: World-line and determinantal quantum monte carlo methods for spins, phonons and electrons, 277–356 (2008) https://doi.org/10. 1007/978-3-540-74686-7_10

2008
[12]

Documentation for the auxiliary-field quantum Monte Carlo code

Assaad, F.F., Bercx, M., Goth, F., Götz, A., Hofmann, J.S., Huffman, E., Liu, Z., Toldin, F.P., Portela, J.S.E., Schwab, J.: The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code. SciPost Phys. Codebases, 1–24 (2025) https://doi.org/10. 21468/SciPostPhysCodeb.1-v2.4

2025
[14]

Inácio, J.a.C., Brink, J., Assaad, F.F., Sato, T.: Finite-temperature fermion Monte Carlo simulations of frustrated spin-Peierls systems. Phys. Rev. B 112, 29 014404 (2025) https://doi.org/10.1103/ssdc-9bsk

work page doi:10.1103/ssdc-9bsk 2025
[16]

Plenum Press, New York (1990)

Mahan, G.D.: Many-Particle Physics, 2nd edn. Plenum Press, New York (1990)

1990
[18]

Identifying the maximum entropy method as a special limit of stochastic analytic continuation

Beach, K.S.D.: Identifying the maximum entropy method as a special limit of stochastic analytic continuation. arXiv e-prints, 0403055 (2004) https://doi.org/ 10.48550/arXiv.cond-mat/0403055 arXiv:cond-mat/0403055 [cond-mat.str-el]

work page internal anchor Pith review doi:10.48550/arxiv.cond-mat/0403055 2004
[19]

Sandvik, A.: Stochastic method for analytic continuation of quantum Monte Carlo data. Phys. Rev. B 57, 10287–10290 (1998) https://doi.org/10.1103/ PhysRevB.57.10287

1998
[20]

Physics Reports 1003, 1–88 (2023) https://doi.org/10.1016/ j.physrep.2022.11.002

Shao, H., Sandvik, A.W.: Progress on stochastic analytic continuation of quantum Monte Carlo data. Physics Reports 1003, 1–88 (2023) https://doi.org/10.1016/ j.physrep.2022.11.002 . Progress on stochastic analytic continuation of quantum Monte Carlo data

2023
[21]

Hicks, C.W., Gibbs, A.S., Mackenzie, A.P., Takatsu, H., Maeno, Y., Yel- land, E.A.: Quantum Oscillations and High Carrier Mobility in the Delafos- site PdCoO2. Phys. Rev. Lett. 109, 116401 (2012) https://doi.org/10.1103/ PhysRevLett.109.116401

2012
[22]

Smidman, M

Mackenzie, A.P.: The properties of ultrapure delafossite metals. Reports on Progress in Physics 80(3), 032501 (2017) https://doi.org/10.1088/1361-6633/ aa50e5

work page doi:10.1088/1361-6633/ 2017
[23]

Nature Communications 8(1), 1152 (2017) https://doi.org/10.1038/ s41467-017-01177-0

Winter, S.M., Riedl, K., Maksimov, P.A., Chernyshev, A.L., Honecker, A., Valentí, R.: Breakdown of magnons in a strongly spin-orbital coupled magnet. Nature Communications 8(1), 1152 (2017) https://doi.org/10.1038/ s41467-017-01177-0

2017
[24]

Chaloupka, J.c.v., Khaliullin, G.: Magnetic anisotropy in the Kitaev model sys- tems Na2IrO3 and RuCl3. Phys. Rev. B 94, 064435 (2016) https://doi.org/10. 1103/PhysRevB.94.064435

2016
[25]

Scientific Reports 6(1), 37925 (2016) https://doi.org/10.1038/ srep37925 30

Yadav, R., Bogdanov, N.A., Katukuri, V.M., Nishimoto, S., Brink, J., Hozoi, L.: Kitaev exchange and field-induced quantum spin-liquid states in honey- comb α-RuCl3. Scientific Reports 6(1), 37925 (2016) https://doi.org/10.1038/ srep37925 30

2016
[26]

Nature Physics 13(11), 1079–1084 (2017) https://doi.org/10.1038/nphys4264

Do, S.-H., Park, S.-Y., Yoshitake, J., Nasu, J., Motome, Y., Kwon, Y.S., Adroja, D.T., Voneshen, D.J., Kim, K., Jang, T.-H., Park, J.-H., Choi, K.-Y., Ji, S.: Majorana fermions in the Kitaev quantum spin system RuCl 3. Nature Physics 13(11), 1079–1084 (2017) https://doi.org/10.1038/nphys4264

work page doi:10.1038/nphys4264 2017
[27]

Bridges and Matthew B

Banerjee, A., Yan, J., Knolle, J., Bridges, C.A., Stone, M.B., Lumsden, M.D., Mandrus, D.G., Tennant, D.A., Moessner, R., Nagler, S.E.: Neutron scattering in the proximate quantum spin liquid α-RuCl3. Science 356(6342), 1055–1059 (2017) https://doi.org/10.1126/science.aah6015

work page doi:10.1126/science.aah6015 2017
[28]

Wu, L., Little, A., Aldape, E.E., Rees, D., Thewalt, E., Lampen-Kelley, P., Baner- jee, A., Bridges, C.A., Yan, J.-Q., Boone, D., Patankar, S., Goldhaber-Gordon, D., Mandrus, D., Nagler, S.E., Altman, E., Orenstein, J.: Field evolution of magnons in α-RuCl3 by high-resolution polarized terahertz spectroscopy. Phys. Rev. B 98, 094425 (2018) https://doi.org...

work page doi:10.1103/physrevb.98.094425 2018
[29]

Möller, M., Maksimov, P.A., Jiang, S., White, S.R., Valentí, R., Chernyshev, A.L.: Rethinking α-RuCl3: Parameters, models, and phase diagram. Phys. Rev. B 112, 104403 (2025) https://doi.org/10.1103/hflp-41lj

work page doi:10.1103/hflp-41lj 2025
[30]

Aaijet al.[LHCb Collaboration]

Sandilands, L.J., Tian, Y., Plumb, K.W., Kim, Y.-J., Burch, K.S.: Scatter- ing Continuum and Possible Fractionalized Excitations in α-RuCl3. Physical Review Letters 114(14), 147201 (2015) https://doi.org/10.1103/PhysRevLett. 114.147201 . Accessed 2024-03-12

work page doi:10.1103/physrevlett 2015
[31]

Nature Communications 12(1), 3513 (2021) https://doi.org/10.1038/ s41467-021-23826-1

Li, H., Zhang, T.T., Said, A., Fabbris, G., Mazzone, D.G., Yan, J.Q., Man- drus, D., Halász, G.B., Okamoto, S., Murakami, S., Dean, M.P.M., Lee, H.N., Miao, H.: Giant phonon anomalies in the proximate Kitaev quantum spin liquid α-RuCl3. Nature Communications 12(1), 3513 (2021) https://doi.org/10.1038/ s41467-021-23826-1 . Accessed 2024-04-24

2021
[32]

Physical Review B 105(12), 121108 (2022) https://doi.org/10.1103/PhysRevB.105.L121108

Feng, K., Swarup, S., Perkins, N.B.: Footprints of Kitaev spin liquid in the Fano lineshape of Raman-active optical phonons. Physical Review B 105(12), 121108 (2022) https://doi.org/10.1103/PhysRevB.105.L121108 . Accessed 2024-03-13

work page doi:10.1103/physrevb.105.l121108 2022
[33]

Nature (2026) https: //doi.org/10.1038/s41586-026-10420-y

Shragai, A., Horsley, E., Kim, S., Kim, Y.-J., Ramshaw, B.J.: Phonon Hall vis- cosity and the intrinsic thermal Hall effect of α-RuCl3. Nature (2026) https: //doi.org/10.1038/s41586-026-10420-y

work page doi:10.1038/s41586-026-10420-y 2026
[34]

Nature 407, 351 (2000)

Schröder, A., Aeppli, G., Coldea, R., Adams, M., Stockert, O., Löhneysen, H.v., Bucher, E., Ramazashvili, R., Coleman, P.: Onset of antiferromagnetism in heavy- fermion metals. Nature 407, 351 (2000)

2000
[35]

Quantum Fisher information in a strange metal

Mazza, F., Biswas, S., Yan, X., Prokofiev, A., Steffens, P., Si, Q., Assaad, F.F., Paschen, S.: Quantum fisher information in a strange metal. arXiv:2403.12779 (2024) arXiv:2403.12779 [cond-mat.str-el] 31

work page internal anchor Pith review Pith/arXiv arXiv 2024
[36]

Imada, M., Fujimori, A., Tokura, Y.: Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998) https://doi.org/10.1103/RevModPhys.70.1039

work page doi:10.1103/revmodphys.70.1039 1998
[37]

Vojta, M.: Orbital-selective mott transitions: Heavy fermions and beyond. J. Low Temp. Phys. 161, 203 (2010)

2010
[38]

Nature Reviews Physics 3(1), 9–26 (2021) https://doi.org/10.1038/s42254-020-00262-6

Paschen, S., Si, Q.: Quantum phases driven by strong correlations. Nature Reviews Physics 3(1), 9–26 (2021) https://doi.org/10.1038/s42254-020-00262-6

work page doi:10.1038/s42254-020-00262-6 2021
[39]

Senthil, T., Sachdev, S., Vojta, M.: Fractionalized fermi liquids. Phys. Rev. Lett. 90(21), 216403 (2003) https://doi.org/10.1103/PhysRevLett.90.216403

work page doi:10.1103/physrevlett.90.216403 2003
[40]

Danu, B., Vojta, M., Assaad, F.F., Grover, T.: Kondo Breakdown in a Spin- 1/2 Chain of Adatoms on a Dirac Semimetal. Phys. Rev. Lett. 125, 206602 (2020) https://doi.org/10.1103/PhysRevLett.125.206602

work page doi:10.1103/physrevlett.125.206602 2020
[41]

Pan and F

Pan, G., Assaad, F.F.: Quantum Monte Carlo studies of U(1) lattice gauge models of Kondo breakdown. arXiv:2512.17801 (2025) arXiv:2512.17801 [cond-mat.str- el]

work page arXiv 2025
[42]

& Imada, M

Aoki, D., Ishida, K., Flouquet, J.: Review of U-based Ferromagnetic Super- conductors: Comparison between UGe2, URhGe, and UCoGe. Journal of the Physical Society of Japan 88(2), 022001 (2019) https://doi.org/10.7566/JPSJ. 88.022001 https://doi.org/10.7566/JPSJ.88.022001

work page doi:10.7566/jpsj 2019
[43]

Nature Physics 15(12), 1250–1254 (2019) https://doi.org/10.1038/s41567-019-0670-x

Ran, S., Liu, I.-L., Eo, Y.S., Campbell, D.J., Neves, P.M., Fuhrman, W.T., Saha, S.R., Eckberg, C., Kim, H., Graf, D., Balakirev, F., Singleton, J., Paglione, J., Butch, N.P.: Extreme magnetic field-boosted superconductivity. Nature Physics 15(12), 1250–1254 (2019) https://doi.org/10.1038/s41567-019-0670-x

work page doi:10.1038/s41567-019-0670-x 2019
[44]

Tokiwa, Y., Opletal, P., Sakai, H., Kambe, S., Yamamoto, E., Kimata, M., Awaji, S., Sasaki, T., Aoki, D., Haga, Y., Tokunaga, Y.: Reinforcement of superconduc- tivity by quantum critical fluctuations of metamagnetism in UTe2. Phys. Rev. B 109, 140502 (2024) https://doi.org/10.1103/PhysRevB.109.L140502

work page doi:10.1103/physrevb.109.l140502 2024
[45]

Tokunaga, Y., Sakai, H., Kambe, S., Opletal, P., Tokiwa, Y., Haga, Y., Kitagawa, S., Ishida, K., Aoki, D., Knebel, G., Lapertot, G., Krämer, S., Horvatić, M.: Lon- gitudinal Spin Fluctuations Driving Field-Reinforced Superconductivity in UTe2. Phys. Rev. Lett. 131, 226503 (2023) https://doi.org/10.1103/PhysRevLett.131. 226503

work page doi:10.1103/physrevlett.131 2023
[46]

Wu, Z., Weinberger, T.I., Hickey, A.J., Chichinadze, D.V., Shaffer, D., Cabala, A., Chen, H., Long, M., Brumm, T.J., Xie, W., Ling, Y., Zhu, Z., Skourski, Y., Graf, D.E., Sechovský, V., Vališka, M., Lonzarich, G.G., Grosche, F.M., Eaton, A.G.: A Quantum Critical Line Bounds the High Field Metamagnetic Transition Surface in UTe2. Phys. Rev. X 15, 021019 (2...

work page doi:10.1103/physrevx.15 2025
[47]

Nature 432, 881 (2004)

Paschen, S., Lühmann, T., Wirth, S., Gegenwart, P., Trovarelli, O., Geibel, C., Steglich, F., Coleman, P., Si, Q.: Hall-effect evolution across a heavy-fermion quantum critical point. Nature 432, 881 (2004)

2004
[48]

Sato, T., Assaad, F.F.: Quantum Monte Carlo simulation of generalized Kitaev models. Phys. Rev. B 104, 081106 (2021) https://doi.org/10.1103/PhysRevB. 104.L081106

work page doi:10.1103/physrevb 2021
[49]

PyTorch: An Imperative Style, High-Performance Deep Learning Library

Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., Chin- tala, S.: PyTorch: An Imperative Style, High-Performance Deep Learning Library (2019). https://arxiv.org/abs/...

work page internal anchor Pith review Pith/arXiv arXiv 2019
[50]

Binder, K.: Finite size scaling analysis of Ising model block distribution func- tions. Z. Phys. B Con. Mat. 43(2), 119–140 (1981) https://doi.org/10.1007/ BF01293604

1981
[51]

Pujari, S., Lang, T.C., Murthy, G., Kaul, R.K.: Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene. Phys. Rev. Lett. 117, 086404 (2016) https://doi.org/10.1103/PhysRevLett.117.086404 33 0.8 1 0.1 0.2 0.3 0.4 L=6 L=9 L=12 T/|J| 0.8 1 0.1 0.2 0.3 0.4 L=6 L=9 L=12 T/|J| (a) FM XXZ model (b) AFM XXZ model RFM RAFM Fig. 7 Corre...

work page doi:10.1103/physrevlett.117.086404 2016