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REVIEW 3 major objections 6 minor 40 references

Quantum annealing of a frustrated magnet

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A tiny transverse field of about 3.5 mK drives a clean frustrated magnet to near its ground state in seconds, where thermal relaxation would take more than 15 hours.

desk verdict First clean magnet showing quantum annealing; the experimental relaxation data are convincing, but the calibration of the tiny transverse field is a calculation, and the QMC sits above the claimed value. read the letter →

arxiv 2411.18167 v1 pith:BTGF6E3G submitted 2024-11-27 cond-mat.str-el cond-mat.mtrl-sci

Yuqian Zhao , Zhaohua Ma , Zhangzhen He , Haijun Liao , Yan-Cheng Wang , Junfeng Wang , Yuesheng Li This is my paper · ORCID
classification cond-mat.str-elcond-mat.mtrl-sci
keywords quantumannealingfrustratedmagnetIsingmodeltransversefieldKosterlitz-Thoulessphasealpha-CoV2O6MonteCarlospinrelaxation
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

This paper claims that the clean frustrated magnet $\alpha$-CoV$_2$O$_6$ exhibits real many-body quantum annealing. Below $\sim 1$ K and in zero transverse field, the Ising spin system stays trapped in metastable Kosterlitz-Thouless phases for at least 15 hours; applying a tiny effective transverse field $\Gamma \approx 3.5$ mK makes it relax toward the lowest-energy state in about 10 seconds, with a nearly temperature-independent relaxation time. The authors argue this is quantum annealing triggered by time-reversal symmetry breaking across the Co$^{2+}$ ground Kramers doublet, not thermal activation, and they reproduce the speed-up qualitatively with stochastic series expansion quantum Monte Carlo simulations of the fitted spin Hamiltonian. If right, it would be the first demonstration of many-body quantum annealing in a structurally clean magnetic material, extending the phenomenon beyond the disordered spin glass LiHo$_x$Y$_{1-x}$F$_4$.

What carries the argument

The machinery is the transverse-field Ising Hamiltonian of $\alpha$-CoV$_2$O$_6$, $$H = J_0 \sum_{\langle i,i_0\rangle} S_i^z S_{i_0}^z + J_1 \sum_{\langle i,i_1\rangle} S_i^z S_{i_1}^z + J_2 \sum_{\langle i,i_2\rangle} S_i^z S_{i_2}^z + J_3 \sum_{\langle i,i_3\rangle} S_i^z S_{i_3}^z - \mu_0 \mu_B H_z g_z \sum_i S_i^z - \Gamma \sum_i S_i^x,$$ whose non-commuting term $\Gamma \sum_i S_i^x$ is the quantum agent. It converts the classical Ising dynamics into a tunnelling problem, and the metastable Kosterlitz-Thouless phases with vortices and antivortices around domain walls are what the tunnelling must escape. The fitted couplings and the single-ion relation between applied transverse field and $\Gamma$ give the model predictive power for both equilibrium and annealing dynamics.

What would settle it

Measure the Co$^{2+}$ ground Kramers-doublet splitting of $\alpha$-CoV$_2$O$_6$ at a transverse field of $\sim 2$ T with high-field ESR or inelastic neutron scattering: if the measured $\Gamma$ is not close to $\sim 3.5$ mK, or if the transverse $g$-factor proves non-negligible, the claimed quantum annealing could instead be classical relaxation.

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Extended reading notes

Core claim

On its own terms, the paper's central discovery is that a transverse field of only $\Gamma \approx 3.5$ mK can anneal a frustrated Ising magnet that would otherwise be frozen: in zero transverse field the longitudinal magnetization shows no approach to the $g_z/6$ plateau even after 15 hours below 1 K, while at the same temperatures a $\sim 2$ T transverse field (whose effective spin-1/2 action is a 3.5 mK transverse term) drives relaxation with $\tau \approx 10$ s. The authors trace this to the transverse-field term $H_{\rm TF} = -\Gamma \sum_i S_i^x$, which breaks time-reversal symmetry, splits the Kramers doublet, and lets individual Co$^{2+}$ spins tunnel between $S_i^z = \pm 1/2$. They fit a spatially anisotropic triangular-lattice Ising Hamiltonian with couplings $J_0 = -30.73$ K, $J_1 = 3.60$ K, $J_2 = 14.21$ K, $J_3 = 2.55$ K, verify its zero-field phases against neutron diffraction, and show with SSE-QMC that tiny transverse fields (0.02--0.1 K) substantially accelerate relaxation at $T \approx 1$ K while changing equilibrium properties negligibly. The conclusion is that $\alpha$-CoV$_2$O$_6$ provides the first example of many-body quantum annealing in a clean frustrated magnet, with the metastable KT phases and their topological defects as the barriers that the tunnelling overcomes.

Load-bearing premise

The entire quantum-annealing interpretation rests on the single-ion mapping that a $\sim 2$ T transverse laboratory field produces only $\Gamma \approx 3.5$ mK of effective transverse coupling in the spin-1/2 Ising model; if the actual transverse $g$-factor or the crystal-field parameters are larger than assumed, the observed fast relaxation could be classical.

Editorial extensions

If this is right

  • A transverse field of a few millikelvin bypasses a roughly 15 K thermal barrier, implying that quantum annealing can outperform thermal annealing by many orders of magnitude in a clean magnet.
  • The relaxation rate at $\Gamma \approx 3.5$ mK is nearly independent of temperature below 1 K, in contrast to the Arrhenius law at zero transverse field, giving a sharp experimental signature that separates quantum from classical relaxation.
  • The same fitted Hamiltonian, with couplings checked against neutron diffraction and thermodynamic data, can be used to predict how other frustrated Ising magnets respond to transverse fields.
  • Heat transport along the frustrated plane is measurably suppressed by transverse fields below 1 K, providing an independent phonon-scattering probe of the domain walls and topological defects released by quantum tunnelling.
  • Even with quantum annealing, the magnetization does not fully reach the exact $g_z/6$ ground-state plateau, showing that residual topological defects or dilute disorder limit complete annealing in a real material.

Reading between the lines

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

  • Beyond the paper: a direct measurement of the Co$^{2+}$ Kramers-doublet splitting at a transverse field of about 2 T, for example by high-field ESR or inelastic neutron scattering, would independently verify the 3.5 mK scale and separate the quantum interpretation from a classical-field artifact.
  • Beyond the paper: because the zero-field magnet sits in KT-like metastable states, $\alpha$-CoV$_2$O$_6$ could serve as a physical testbed for the out-of-equilibrium topological-defect dynamics studied in programmable quantum annealers, bridging real-materials and simulator results.
  • Beyond the paper: the incomplete annealing after hours suggests that protocol design, such as field cycling or a temperature quench before applying the transverse field, might push the system closer to the exact ground state; that is a testable prediction about the role of history in annealing efficiency.
  • Beyond the paper: a systematic comparison of the ratio $\Gamma/\Delta E$ across clean frustrated Ising magnets could identify a practical rule for which compounds show observable many-body quantum annealing at achievable transverse fields.
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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 reports magnetization and heat transport measurements on single crystals of α-CoV2O6, an Ising-like frustrated magnet. The authors find that below ~1 K in zero transverse field the longitudinal magnetization remains frozen in a metastable state for at least 15 hours, whereas applying a transverse field of about 2 T (claimed to create an effective transverse field Γ≈3.5 mK) yields relaxation toward the 1/3-plateau value with a nearly temperature-independent time constant τ~10 s. The temperature-independent relaxation is interpreted as quantum annealing driven by a tiny non-commuting field, and the authors support this with SSE-QMC simulations of the fitted spin Hamiltonian at Γ≥0.02 K. The paper argues this is the first observation of many-body quantum annealing in a structurally clean frustrated magnet.

Significance. The experimental observation of a drastic, nearly temperature-independent speed-up of relaxation under a transverse field, contrasted with a diverging Arrhenius relaxation time at zero field, is a significant and potentially influential result. If the interpretation holds, it extends quantum annealing phenomena beyond the disordered LiHoxY1-xF4 system to a structurally clean frustrated magnet and provides a concrete material platform for further studies. The paper is commendable for including extensive experimental data, openly describing limitations of the numerical simulations, and making explicit statements about the incompleteness of annealing and the possible role of defects. The central experimental result is robust and warrants publication, but the quantitative calibration of the effective transverse field is not fully established, and the numerical support is qualitative rather than at the claimed experimental parameter.

major comments (3)
  1. [Spin Hamiltonian, Eq. (1) and Fig. 1c] The calibration of the applied transverse field to the effective Γ is the load-bearing link of the paper. The main text states gx∼gy∼0 and Γ≈3.5 mK at μ0Hx≈2 T based on a single-ion Hamiltonian in Supplementary Note 2, but gx≈0 is not presented as a measured bound. If gx were as large as 0.01–0.1, the linear Zeeman term gx μB Hx Sx would contribute 7–70 mK, changing the claimed 'tiny field' by one to two orders of magnitude. The agreement of TN(Hx) with the calculated Γ (Fig. 1c) does not uniquely determine Γ, and the authors should either provide an experimental bound on gx or quantify the uncertainty in the single-ion mapping. Without this, the central quantitative claim that Γ≈3.5 mK triggers quantum annealing is not secure.
  2. [Quantum Monte Carlo simulations, Fig. 4] The numerical simulations are carried out only at Γ≥0.02 K, whereas the experimental claim is made for Γ≈3.5 mK, an order of magnitude smaller. The paper explicitly acknowledges that 'observing clear QA effects at 0 < Γ < 0.02 K remains extremely challenging' and that the numerical results 'only seek to provide a qualitative interpretation.' Consequently, the microscopic model is never directly tested at the experimentally claimed parameter. The qualitative support is welcome, but the extrapolation over a factor of roughly six in Γ is not demonstrated. The authors should either extend the simulations to lower Γ using more efficient or specialized methods, or clearly state that the quantitative relation between Γ and the relaxation process is not directly verified.
  3. [Quantum Monte Carlo simulations / Discussion] The authors state that the microscopic model 'may lack high precision in simulating the slow spin dynamics observed in α-CoV2O6, especially at smaller transverse fields (0 < Γ < 0.02 K).' Combined with the fact that the exchange parameters J0–J3 are fitted to quasi-equilibrium thermodynamic data of the same material, this limits the predictive value of the simulations for the out-of-equilibrium annealing dynamics. The experimental observation stands on its own, but the interpretation as quantum annealing with a specific Γ would be strengthened by an independent constraint on Γ and by an explicit discussion of whether classical mechanisms (e.g., a nonzero gx) could reproduce the temperature-independent relaxation.
minor comments (6)
  1. [Spin Hamiltonian] The statement 'gx ∼ gy ∼ 0' should be replaced by an explicit upper bound (e.g., |gx| < 0.01 or a similar measured limit) with a reference to the underlying determination, so that readers can assess the error in Γ.
  2. [Fig. 3b] The temperature range and goodness-of-fit for the constant red-line fit to τ^{-1} at low temperatures are not stated in the main text; please add these details.
  3. [Results] There is a typo in the Results section: 'the reduce of annealing timeτ' should read 'the reduction of annealing time τ'; also, 'slight derivations from the T^3 law' should read 'slight deviations'.
  4. [Fig. 1b and related text] The term 'inner gap' for Γ is unconventional; consider using 'tunnel splitting' or 'transverse-field-induced splitting' to avoid confusion with the crystal-field gap E3−E1.
  5. [Fig. 4c] The molecular-field estimate of W↓/W↑ is a single-site approximation; the text should clarify that this is not a many-body result and that the SSE-QMC results are the relevant many-body evidence.
  6. [Methods] The paper should state explicitly the measurement uncertainty in the transverse-field angle θ and how it propagates to Hx and Hz, since the claimed Γ≈3.5 mK is sensitive to small misalignments.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fitted exchange couplings calibrate the equilibrium model, while the annealing dynamics and transverse-field scale are independent tests or stated limitations, not constructed predictions.

full rationale

The derivation chain is not circular. The exchange couplings J0-J3 in Eq. (1) are fitted to quasi-equilibrium thermodynamic data above 1.9 K at Gamma = 0, and the same Hamiltonian is then used in SSE-QMC to simulate out-of-equilibrium relaxation. This is model calibration followed by a dynamical test: the relaxation times, their temperature independence under transverse field, and the Monte Carlo step dependence are not fit targets, so the annealing behavior is not forced by construction. The transverse-field scale Gamma ~ 3.5 mK at mu0 Hx ~ 2 T comes from a single-ion calculation with crystal-electric-field parameters and is checked against the TN(H_perp) suppression (Fig. 1c), not fitted to the relaxation data. The paper explicitly states that QMC cannot access Gamma < 0.02 K: 'observing clear QA effects at 0 < Gamma < 0.02 K remains extremely challenging', so the many-body simulations are qualitative at 0.02 <= Gamma <= 0.1 K, not a re-statement of the 3.5 mK experiment; this is a scope limitation, not circularity. The self-citations [14,25,31] concern the standard transverse-field operator and strong Ising anisotropy and are not load-bearing, since the transverse-field term is independently derived in Supplementary Note 2. The central observed facts (15-hour freezing at Hx ~ 0, tau ~ 10 s at Hx ~ 2 T) are experimental inputs that the model does not define, so no fitted parameter is renamed as a prediction.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim relies on the fitted Ising Hamiltonian (Eq. 1), the single-ion mapping from applied transverse field to Γ, and the assumption that QMC update steps represent physical time. The four exchange couplings are free parameters fitted to thermodynamic data; the Γ-Hx mapping is also effectively fitted to the observed TN suppression. No new physical entities are introduced.

free parameters (6)
  • J0 (intrachain ferromagnetic coupling) = -30.73 K
    Fitted to quasi-equilibrium thermodynamic data above 1.9 K; used in Eq. (1) and all QMC simulations.
  • J1, J2, J3 (interchain couplings) = 3.60 K, 14.21 K, 2.55 K
    Refined together with J0 by fitting thermodynamic data (Supplementary Table 1, Figs. 5, 6).
  • Effective transverse field Γ vs applied Hx = 3.5 mK at Hx ~ 2 T
    Derived from single-ion Hamiltonian in Supplementary Note 2; the paper uses this mapping to compare experiments with simulations, but the full calculation is not in the main text.
  • Mean field h in molecular-field estimate = |J0| = 30.73 K
    Used in Hs = -hSz - ΓSx to estimate spin-flip ratios; h is set to the dominant coupling, a rough approximation.
  • Barrier energy ΔE and attempt rate 1/τm = 15.3 K; 1.5 Hz
    Arrhenius fit to zero-field relaxation rates; used to show thermal annealing becomes impossible at low T.
  • Debye temperature Θ_D = 160 K
    Fitted from specific heat of nonmagnetic α-ZnV2O6; used to model phonon thermal conductivity.
assumptions (5)
  • domain assumption The effective spin-1/2 Ising Hamiltonian of Eq. (1) with couplings J0-J3 and transverse field -ΓΣSx captures the low-energy physics of α-CoV2O6.
    Invoked throughout the paper to interpret all experiments and simulations; the parameters are fitted to the same material's data.
  • ad hoc to paper Transverse field effects are fully captured by the gap Γ introduced by the single-ion Hamiltonian, with g_x~0 so no classical coupling of the transverse field to the magnetic moment along z.
    This is the crux of the QA interpretation; if g_x were non-negligible, the transverse field would classically tilt spins and could explain relaxation without quantum tunneling.
  • domain assumption The QMC Markov-chain updates (MCS) can be used as a proxy for physical time, so that the MCS dependence of energy and magnetization represents the annealing dynamics.
    The paper uses 'SSE MCS' as a time axis in Fig. 4; this is a common but uncontrolled mapping for real-time dynamics.
  • domain assumption The system initializes in a fully-inversely-polarized state at -4.2 T, and the subsequent relaxation is measured from the moment Hz reaches 2 T.
    Experiments and simulations both assume this initialization is achieved quickly; if the transverse field perturbs the polarization, the initial state would be different.
  • standard math The Kramers doublet is well separated (E3-E1~140 K), allowing the effective spin-1/2 description.
    Justifies the Ising model; standard in crystal-field analysis.

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Cite this review

Pith. "Pith review of Quantum annealing of a frustrated magnet." pith.science (2026). https://pith.science/paper/BTGF6E3G

@misc{pith2026241118167,
  author       = {Pith},
  title        = {Pith review of: Quantum annealing of a frustrated magnet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BTGF6E3G}},
  note         = {Machine review of arXiv:2411.18167}
}
abstract

Quantum annealing, which involves quantum tunnelling among possible solutions, has state-of-the-art applications not only in quickly finding the lowest-energy configuration of a complex system, but also in quantum computing. Here we report a single-crystal study of the frustrated magnet $\alpha$-CoV$_2$O$_6$, consisting of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder. We observe quantum annealing phenomena resulting from time-reversal symmetry breaking in a tiny transverse field. Below $\sim$ 1 K, the system exhibits no indication of approaching the lowest-energy state for at least 15 hours in zero transverse field, but quickly converges towards that configuration with a nearly temperature-independent relaxation time of $\sim$ 10 seconds in a transverse field of $\sim$ 3.5 mK. Our many-body simulations show qualitative agreement with the experimental results, and suggest that a tiny transverse field can profoundly enhance quantum spin fluctuations, triggering rapid quantum annealing process from topological metastable Kosterlitz-Thouless phases, at low temperatures.

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Works this paper leans on

40 extracted references · 19 canonical work pages

  1. [1]

    Biamonte, J. et al. Quantum machine learning. Nature 549, 195–202 (2017). URL https://www.nature.com/articles/nature23474

    work page 2017

  2. [2]

    & Schmitt, S

    Yarkoni, S., Raponi, E., B¨ ack, T. & Schmitt, S. Quantum annealing for industry applications: Introduction and review. Rep. Prog. Phys. 85, 104001 (2022). https://doi.org/10.1088/1361-6633/ac8c54

    doi:10.1088/1361-6633/ac8c54 2022

  3. [3]

    E., Martoˇ n´ ak, R., Tosatti, E

    Santoro, G. E., Martoˇ n´ ak, R., Tosatti, E. & Car, R. Theory of quantum annealing of an Ising spin glass. Science 295, 2427–2430 (2002). https: //doi.org/10.1126/science.1068774

    doi:10.1126/science.1068774 2002

  4. [4]

    Johnson, M. W. et al. Quantum annealing with manufactured spins. Nature 473, 194–198 (2011). https://doi.org/10.1038/nature10012

    doi:10.1038/nature10012 2011

  5. [5]

    Zhang, J. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017). https: //doi.org/10.1038/nature24654

    doi:10.1038/nature24654 2017

  6. [6]

    King, A. D. et al. Observation of topological phenomena in a pro- grammable lattice of 1,800 qubits. Nature 560, 456–460 (2018). https: //doi.org/10.1038/s41586-018-0410-x

    doi:10.1038/s41586-018-0410-x 2018

  7. [7]

    Harris, R. et al. Phase transitions in a programmable quantum spin glass simulator. Science 361, 162–165 (2018). https://doi.org/10.1126/science. aat2025

    doi:10.1126/science 2018

  8. [8]

    & Guo, H

    Ocampo-Alfaro, P. & Guo, H. Cooling-rate dependence of the ground- state energy using microcanonical simulated annealing. Phys. Rev. E 53, 1982–1985 (1996). https://doi.org/10.1103/PhysRevE.53.1982

    work page doi:10.1103/physreve.53.1982 1996

Show all 40 references
  1. [9]

    Brooke, J., Bitko, D., Rosenbaum, T. F. & Aeppli, G. Quantum annealing of a disordered magnet. Science 284, 779–781 (1999). https://doi.org/ 10.1126/science.284.5415.779

    1999 doi

  2. [10]

    Labuhn, H. et al. Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models. Nature 534, 667–670 (2016). https: //doi.org/10.1038/nature18274 . Springer Nature 2021 LATEX template Quantum annealing of a frustrated magnet 13

    2016 doi

  3. [11]

    Bernien, H. et al. Probing many-body dynamics on a 51-atom quan- tum simulator. Nature 551, 579–584 (2017). https://doi.org/10.1038/ nature24622

    2017

  4. [12]

    Li, Y. et al. Crystalline electric-field randomness in the triangular lattice spin-liquid YbMgGaO 4. Phys. Rev. Lett. 118, 107202 (2017). https: //doi.org/10.1103/PhysRevLett.118.107202

    2017 doi

  5. [13]

    Liu, J. et al. Gapless spin liquid behavior in a kagome Heisenberg antiferromagnet with randomly distributed hexagons of alternate bonds. Phys. Rev. B 105, 024418 (2022). https://doi.org/10.1103/PhysRevB. 105.024418

    2022 doi

  6. [14]

    Li, Y. et al. Partial up-up-down order with the continuously distributed order parameter in the triangular antiferromagnet TmMgGaO 4. Phys. Rev. X 10, 011007 (2020). https://doi.org/10.1103/PhysRevX.10.011007

    2020 doi

  7. [15]

    Broholm, C. et al. Quantum spin liquids. Science 367, eaay0668 (2020). URL https://science.sciencemag.org/content/367/6475/eaay0668

    2020

  8. [16]

    Brooke, J., Rosenbaum, T. F. & Aeppli, G. Tunable quantum tunnelling of magnetic domain walls. Nature 413, 610–613 (2001). URL https: //www.nature.com/articles/35098037

    2001

  9. [17]

    & Chakrabarti, B

    Das, A. & Chakrabarti, B. K. Colloquium: Quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061–1081 (2008). https: //doi.org/10.1103/RevModPhys.80.1061

    2008 doi

  10. [18]

    King, A. D. et al. Quantum annealing simulation of out-of-equilibrium magnetization in a spin-chain compound. PRX Quantum 2, 030317 (2021). https://doi.org/10.1103/PRXQuantum.2.030317

    2021 doi

  11. [19]

    Nekrashevich, I. et al. Reaching the equilibrium state of the frustrated triangular Ising magnet Ca 3Co2O6. Phys. Rev. B 105, 024426 (2022). https://doi.org/10.1103/PhysRevB.105.024426

    2022 doi

  12. [20]

    Lenertz, M. et al. Magnetic structure of ground and field-induced ordered states of low-dimensional α-CoV2O6: Experiment and theory. Phys. Rev. B 86, 214428 (2012). https://doi.org/10.1103/PhysRevB.86.214428

    2012 doi

  13. [21]

    & Radtke, G

    Sa´ ul, A., Vodenicarevic, D. & Radtke, G. Theoretical study of the mag- netic order in α-CoV2O6. Phys. Rev. B 87, 024403 (2013). https: //doi.org/10.1103/physrevb.87.024403

    2013 doi

  14. [22]

    & Cheng, W

    He, Z., Yamaura, J.-I., Ueda, Y. & Cheng, W. CoV 2O6 single crys- tals grown in a closed crucible: unusual magnetic behaviors with large Springer Nature 2021 LATEX template 14 Quantum annealing of a frustrated magnet anisotropy and 1 3 magnetization plateau. J. Am. Chem. Soc. ...

    2009 doi

  15. [23]

    Berezinski ˇi, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. quantum systems. Sov. Phys. JETP 34, 610–616 (1972). URL https: //inspirehep.net/files/0f7b50c47ec26bed99a50ff199960259

    1972

  16. [24]

    Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C: Solid State Phys. 6, 1181–1203 (1973). https://doi.org/10.1088/0022-3719/6/7/010

    1973 doi

  17. [25]

    Li, Y. et al. Spin dynamics and Griffiths singularity in the random quan- tum Ising magnet PrTiNbO 6. npj Quantum Mater. 6, 34 (2021). URL https://doi.org/10.1038/s41535-021-00333-6

    2021 doi

  18. [26]

    Silevitch, D. M. et al. A ferromagnet in a continuously tunable random field. Nature 448, 567–570 (2007). https://doi.org/10.1038/nature06050

    2007 doi

  19. [27]

    C., Ouyang, Z

    Sun, Y. C., Ouyang, Z. W., Shu, H., Xia, Z. C. & Rao, G. Metastable 1/3 magnetization plateau and memory effects in spin-chain compound α-CoV2O6. Appl. Phys. A 122, 832 (2016). https://doi.org/10.1007/ s00339-016-0344-9

    2016

  20. [28]

    Sandvik, A. W. Stochastic series expansion method for quantum Ising models with arbitrary interactions. Phys. Rev. E 68, 056701 (2003). https://doi.org/10.1103/PhysRevE.68.056701

    2003 doi

  21. [29]

    Liao, Y. D. et al. Phase diagram of the quantum Ising model on a tri- angular lattice under external field. Phys. Rev. B 103, 104416 (2021). https://doi.org/10.1103/PhysRevB.103.104416

    2021 doi

  22. [30]

    M., Guaita, T., Shi, T., Demler, E

    Schindler, P. M., Guaita, T., Shi, T., Demler, E. & Cirac, J. I. Varia- tional ansatz for the ground state of the quantum Sherrington-Kirkpatrick model. Phys. Rev. Lett. 129, 220401 (2022). https://doi.org/10.1103/ PhysRevLett.129.220401

    2022

  23. [31]

    Li, Y., Bachus, S., Tokiwa, Y., Tsirlin, A. A. & Gegenwart, P. Gapped ground state in the zigzag pseudospin-1/2 quantum antiferromagnetic chain compound PrTiNbO 6. Phys. Rev. B 97, 184434 (2018). https: //doi.org/10.1103/PhysRevB.97.184434

    2018 doi

  24. [32]

    & Giordano, N

    Hong, K. & Giordano, N. Evidence for domain wall tunnelling in a quasi- one dimensional ferromagnet. J. Phys.: Condens. Matter 8, L301–L306 (1996). https://doi.org/10.1088/0953-8984/8/19/001 . Springer Nature 2021 LATEX template Quantum annealing of a frustrated magnet 15

    1996 doi

  25. [33]

    Hong, X. et al. Heat transport of the kagome Heisenberg quantum spin liquid candidate YCu 3(OH)6.5Br2.5: Localized magnetic excitations and a putative spin gap. Phys. Rev. B 106, L220406 (2022). https://doi.org/ 10.1103/PhysRevB.106.L220406

    2022 doi

  26. [34]

    Yu, Y. J. et al. Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet RuCl3 across the field-induced phase transition. Phys. Rev. Lett. 120, 067202 (2018). https://doi.org/10.1103/PhysRevLett.120. 067202

    2018 doi

  27. [35]

    Gu, C. C. et al. Field-driven quantum criticality in the spinel magnet ZnCr2Se4. Phys. Rev. Lett. 120, 147204 (2018). https://doi.org/10.1103/ PhysRevLett.120.147204

    2018

  28. [36]

    Watanabe, D. et al. Emergence of nontrivial magnetic excitations in a spin-liquid state of kagom´ e volborthite. Proc. Natl. Acad. Sci. 113, 8653–8657 (2016). https://doi.org/10.1073/pnas.1524076113

    2016 doi

  29. [37]

    Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangu- lar quantum Ising material TmMgGaO4. Nat. Commun. 11, 1111 (2020). https://doi.org/10.1038/s41467-020-14907-8

    2020 doi

  30. [38]

    & Chen, G

    Liu, C., Huang, C.-J. & Chen, G. Intrinsic quantum Ising model on a triangular lattice magnet TmMgGaO4. Phys. Rev. Res. 2, 043013 (2020). https://doi.org/10.1103/PhysRevResearch.2.043013

    2020 doi

  31. [39]

    Shimizu, Y. et al. Development of high-resolution capacitive Faraday mag- netometers for sub-Kelvin region. Rev. Sci. Instrum. 92, 123908 (2021). https://doi.org/10.1063/5.0067759

    2021 doi

  32. [40]

    Li, Y. et al. Rearrangement of uncorrelated valence bonds evidenced by low-energy spin excitations in YbMgGaO 4. Phys. Rev. Lett. 122, 137201 (2019). https://doi.org/10.1103/PhysRevLett.122.137201 . Acknowledgments We gratefully acknowledge Jun Li and Xiaochen Hong for their t...

    2019 doi

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