Pith. sign in

REVIEW 3 major objections 5 minor 74 references

Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read A magnetic field can drive a two-dimensional quantum antiferromagnet into an effective one-dimensional spin chain regime, a quantum Monte Carlo study of botallackite shows.

desk verdict First dynamical QMC evidence for field-driven dimensional reduction in a 2D spin model; solid as a model result, but the botallackite-specific claim rests on omitted anisotropy. read the letter →

arxiv 2608.04096 v1 pith:MBPVCV44 submitted 2026-08-04 cond-mat.str-el

Subhankar Khatua , Marcin Raczkowski , Jeroen van den Brink , Fakher F. Assaad This is my paper · ORCID
classification cond-mat.str-el
keywords dimensionalreductionquantumantiferromagnetspin-1/2Heisenbergchaintwo-spinoncontinuumbotallackiteMonteCarloinelasticneutronscatteringmagneticfieldcontrol
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 shows that an applied magnetic field can itself reduce the effective dimensionality of a quantum magnet, without the low dimensionality having to be baked into the crystal by strongly anisotropic couplings. The setup is a two-dimensional spin-1/2 model for the mineral botallackite, made of alternating ferromagnetic and antiferromagnetic chains coupled by interchain exchange. Above a critical field of about 16 tesla the ferromagnetic chains fully polarize and stiffen, so transverse spin fluctuations on the antiferromagnetic chains can no longer travel from one chain to the next. The paper's quantum Monte Carlo spectra show that the low-energy magnetic response then becomes that of a one-dimensional Heisenberg antiferromagnetic spin-1/2 chain in a field: a gapless, incommensurate two-spinon continuum. If this is right, a continuous external field is a way to switch effective dimensionality, and neutron scattering can look for the predicted signatures in real materials.

What carries the argument

The central object is the two-dimensional Heisenberg Hamiltonian with alternating FM ($J_1 = -0.3 J_2$) and AFM ($J_2 = 5.3$ meV) chains, interchain couplings $J_3 = 0.2 J_2$ and $J_4 \approx 0$, and $g=2.24$, in an out-of-plane magnetic field. The mechanism carrying the argument is the field-induced polarization and stiffening of the FM chains: their transverse spin fluctuations acquire a Zeeman gap that grows with field, making them inert at low energies and unable to transmit AFM fluctuations between neighboring AFM chains. The identifying signature is the dynamical structure factor of the AFM chains, which evolves in the plateau regime into the gapless, incommensurate two-spinon continuum characteristic of a partially polarized one-dimensional spin-1/2 Heisenberg antiferromagnet; a spinon continuum is the band of fractional spin-1/2 excitations that is the hallmark of such chains. A parton mean-field treatment with fermionic spinons reproduces the field-dependent incommensurate wavevectors through Zeeman-shifted spinon bands.

What would settle it

Neutron scattering on botallackite in the 16–97 T range would settle the material-specific claim: the paper predicts a gapless, incommensurate two-spinon continuum with flat dispersion perpendicular to the chains, so observing a gapped interchain magnon mode, or a discrete $E_8$ ladder instead of a continuum, would falsify it.

Watch

Extended reading notes

Core claim

The central claim, stated on the paper's own terms, is that a two-dimensional SU(2)-symmetric Heisenberg model with alternating ferromagnetic ($J_1$) and antiferromagnetic ($J_2$) spin-1/2 chains — the model proposed for botallackite, Cu$_2$(OH)$_3$Br — undergoes a magnetic-field-driven dimensional reduction. Above the critical field $B_c \approx 16$ T the ferromagnetic chains are almost fully polarized while the antiferromagnetic chains remain canted, and the low-energy dynamics of the antiferromagnetic chains become those of decoupled one-dimensional Heisenberg antiferromagnetic chains in a magnetic field. The evidence is dynamical structure factors computed with finite-temperature auxiliary-field quantum Monte Carlo on a 12×6 lattice of four-orbital unit cells: beyond $B_c$ the two-spinon continuum becomes almost gapless, the dispersion flattens in the interchain direction, and at higher fields the transverse and longitudinal spectra develop the field-dependent incommensurate features of a partially polarized spin-1/2 chain. A parton mean-field calculation with Zeeman-shifted spinon bands reproduces the field-dependent wavevectors. The authors note that the model omits the FM-chain exchange anisotropy and Dzyaloshinskii-Moriya interactions, which could alter the material-specific spectrum, but they present the dimensional-reduction mechanism itself as generic to the alternating-chain structure.

Load-bearing premise

The material-specific prediction assumes the omitted FM-chain exchange anisotropy and Dzyaloshinskii-Moriya interactions are genuinely negligible; if they are not, the field-polarized FM chains would behave as an Ising model with a different (possibly $E_8$) spectrum, altering the predicted neutron-scattering signatures even if the general dimensional-reduction idea survives.

Editorial extensions

If this is right

  • Above $B_c \approx 16$ T and below the saturation field $B_s \approx 97$ T, the model's low-energy physics is that of decoupled one-dimensional Heisenberg antiferromagnetic chains in a field, so the magnetic field acts as a continuous dimensional-reduction control parameter.
  • The predicted spectra give distinct inelastic-neutron-scattering signatures: a gapless incommensurate two-spinon continuum, with a transverse mode near zero wavevector that shifts with field and a longitudinal peak that moves away from the commensurate AFM wavevector.
  • The FM chains' transverse magnon gap grows with field, which suppresses the effect of the interchain coupling $J_3$ at low energies; the crossover is driven by field rather than by temperature.
  • Because the mechanism relies on the alternating FM/AFM chain structure and the hierarchy $J_2 > J_1 > J_3$, field control of dimensionality should be a general route in other magnets with the same arrangement of chains.

Reading between the lines

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

  • A quantitative criterion the paper does not spell out: the crossover should occur once the field-induced Zeeman gap on the FM chains (set by $B$ and $J_1$) exceeds the interchain coupling $J_3$; this predicts that $B_c$ shifts when $J_3$ or $J_1$ is varied in the model.
  • The authors' caveat about omitted terms suggests a discriminating experiment: if botallackite's FM chains are Ising-like, the same field range may show an $E_8$ bound-state ladder rather than a spinon continuum, so high-resolution neutron scattering could distinguish the two scenarios.
  • A consequence of the parton picture is that the incommensurate wavevectors track the AFM-chain magnetization; measuring them as a function of field would effectively read out the AFM sublattice magnetization separately from the total magnetization.
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 / 5 minor

Summary. The manuscript studies a spin-1/2 Heisenberg model on a square lattice with alternating ferromagnetic (J1) and antiferromagnetic (J2) chains coupled through interchain couplings J3 and J4, motivated by the layered mineral botallackite, Cu2(OH)3Br. Using sign-problem-free auxiliary-field quantum Monte Carlo simulations combined with stochastic analytic continuation, the authors compute the field-dependent magnetization and the dynamical structure factors of the AFM- and FM-chain sectors. They find that above B_c ≈ 16 T the FM chains are fully polarized and the low-energy AFM-chain response develops the hallmarks of a one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field: a two-spinon continuum, an additional gapless mode near zero wavevector in the transverse channel, and field-dependent incommensurate shifts of the spectral weight in both transverse and longitudinal channels. A parton mean-field calculation of a single chain reproduces the qualitative incommensurate wavevector shifts. The authors conclude that a magnetic field can drive a dimensional reduction from two-dimensional to one-dimensional spin dynamics and propose inelastic neutron scattering signatures for botallackite.

Significance. If the central claim holds, the paper provides a concrete and conceptually novel example of a control parameter—rather than spatial anisotropy—driving a crossover from two-dimensional to one-dimensional spin dynamics, with clear spectroscopic consequences. The numerics are based on an unbiased, sign-problem-free QMC method, and the comparison with 1D physics uses multiple independent features (flat dispersion along the interchain direction, gapped FM response, incommensurate mode positions) rather than a single fitted quantity. The parton mean-field analysis is self-contained and is checked against known 1D chain behavior. The static structure factor analysis in Fig. 5 adds a quantitative, if energy-integrated, confirmation of the incommensurate shifts. However, the evidence for the central dimensional-reduction claim is presently qualitative: finite-temperature broadening, finite-size effects, and the absence of a quantitative bound on residual interchain coupling leave room for an alternative interpretation, and the material-specific prediction is weakened by the model's acknowledged omission of exchange anisotropy and Dzyaloshinskii-Moriya interactions.

major comments (3)
  1. [Fig. 4 and the zero-field discussion in the main text] The claim that beyond B_c ≈ 16 T the low-energy spectrum 'approaches that of an AFM chain' rests on the visual resemblance of the QMC spectra to the decoupled-chain spectra of Fig. 3, but no quantitative measure of the residual interchain coupling is provided. This is load-bearing because the authors themselves note that at zero field the effective interchain scale (J3)^2/J2 = 0.212 meV ≈ 2.46 K is already smaller than the simulation temperature k_B T = 3.074 K = 0.265 meV, so that the spin-wave velocity cannot be resolved. Above B_c the interchain coupling is expected to be further reduced, and a continuum that appears 'almost gapless' at B ≈ 22 T may reflect thermal broadening rather than a field-driven suppression of interchain propagation. Please add a quantitative diagnostic, for example the q_y width of the low-energy spectral weight at fixed q_x and ω, the field dependence of the low-energy edge of S_AFM^xy([20],ω), or the interchain spin-correlation length, and compare it with the decoupled-chain result at the same temperature and field.
  2. [Fig. 3 versus Fig. 4] The reference decoupled-chain calculation in Fig. 3 is carried out at B = 36.625 T, whereas the claimed onset of dimensional reduction is identified already at B ≈ 22 T in Figs. 4(b) and 4(f). The field-dependent incommensurate features at higher fields are more distinctive, but the direct mapping onto a 1D chain at the crossover field is asserted by eye. A quantitative comparison at matched field and temperature—for example, the normalized difference between the full model's AFM-chain S(q,ω) and the decoupled-chain S(q,ω) over a low-energy window—would establish that the full model's response is the 1D chain response rather than a thermally broadened 2D response. The AFM-chain Fourier transform in the full model also involves the orbital positions, so an apples-to-apples comparison with the elementary 1D chain calculation is not automatic.
  3. [Discussion and Conclusions] The abstract and concluding paragraph state that the model 'provides clear signatures for inelastic neutron scattering' for botallackite, yet the Discussion explicitly acknowledges that the modeling 'omits an exchange anisotropy that is dominant in the FM chain, as well as Dzyaloshinskii-Moriya interactions,' and that recent experiments (Ref. [44]) are interpreted along E8 lines. These omissions are not merely cosmetic: if the FM-chain anisotropy is dominant, the field-polarized FM chains would be described by a transverse-field Ising model, and the low-energy spectrum near the polarization crossover could contain confined-spinon or E8 features rather than the SU(2) two-spinon continuum predicted here. The material-specific prediction therefore needs to be either softened or supported by a quantitative estimate of the effect of these terms on the computed dynamical structure factors.
minor comments (5)
  1. [Fig. 4 and text near 'almost gapless'] The phrases 'almost gapless' and 'essentially flat' are used without an operational definition; please specify the energy threshold below which the spectral weight is considered gapless and the q_y bandwidth below which the dispersion is considered flat at the energy scale of interest.
  2. [End Matter, Eq. (7)] The parton mean-field calculation reports the self-consistent value χ = 1.541 meV for J = 5.3 meV, B = 20 T, and β = 20 meV^-1, but the magnetization implied by this saddle-point solution is not given; providing it would allow a direct comparison with the QMC magnetization of the AFM chains at the same field.
  3. [Figs. 2 and 4 captions] The color scale is logarithmic and no error bars or representative statistical uncertainties are shown for the analytically continued spectra; adding error estimates, at least for the specific constant-ω cuts used to support the flat-dispersion claim, would strengthen the presentation.
  4. [Eqs. (8) and (9)] The Fermi occupation factors in the parton mean-field susceptibilities require a chemical potential to enforce the single-occupancy constraint on average; please state explicitly how the Fermi level is determined in the saddle-point solution.
  5. [References] Reference [44] is a very recent preprint and is used to motivate the E8 discussion; if a published version becomes available, it should be cited, and otherwise the sentence should make clear that the E8 interpretation is an ongoing experimental discussion.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: unbiased QMC dynamics independently test the 1D-chain dimensional-reduction proposal.

full rationale

The central claim is that beyond B_c ≈ 16 T the dynamical structure factor of the 2D botallackite model approaches that of a 1D AFM Heisenberg chain. The evidence is produced by finite-temperature auxiliary-field QMC on the full 2D Hamiltonian (Eq. 1), which is numerically exact and sign-problem-free; no parameter of the 2D calculation is fitted to the 1D spectrum. The comparison target is an independent QMC calculation of decoupled chains (J3 = 0, Fig. 3) plus known Bethe-ansatz/1D-chain results (Refs. [31–37]), and the parton mean-field theory (End Matter) is solved with its own self-consistency condition and checked against the chain QMC; it is not used to generate the full-model spectra. Self-citations (Refs. [17,18,22,44,50]) supply model parameters, the ALF code, and the original dimensional-reduction proposal, but the dynamical QMC result stands independently: the paper's new S(q,ω) data are not derived from those citations. The skeptic's concern that the apparent gapless/flat dispersion may reflect finite-temperature broadening rather than true interchain decoupling is a quantitative-evidence or correctness issue, not a circularity: it does not amount to the prediction being equivalent to an input by construction. Accordingly, no circular step is identified.

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

No free parameters are fitted in this paper; all model parameters are taken from prior experimental estimates. The central claim rests on the chosen Hamiltonian, the parameter hierarchy, the validity of the QMC and analytic continuation methods, and the adequacy of the finite cluster. No new entities are introduced.

assumptions (5)
  • domain assumption The spin Hamiltonian of Eq. (1) with experimentally estimated couplings J2=5.3 meV, J1=-0.3J2, J3=0.2J2, J4≈0, g=2.24 captures the magnetic properties of botallackite.
    The model omits exchange anisotropy and Dzyaloshinskii-Moriya interactions; the authors argue they are negligible but acknowledge the simplification in the Discussion. The material-specific claim depends on this.
  • domain assumption The hierarchy J2 > |J1| > J3 ensures that an applied field polarizes the FM chains first, while the AFM chains remain canted.
    This hierarchy is essential for the proposed mechanism; it is taken from parameter estimates in Refs. [17,18].
  • standard math The auxiliary-field QMC with a finite Hubbard constraint U/J2=1 faithfully imposes single-occupancy and is free of the negative-sign problem.
    Standard ALF implementation; sign-problem-free for the unfrustrated model; validation via ⟨(n-1)^2⟩≈0.
  • domain assumption Stochastic analytical continuation of imaginary-time correlation functions yields reliable real-frequency dynamical structure factors at the energy scales of interest.
    Analytic continuation is ill-conditioned; qualitative features (gapless continuum, incommensurability) are robust, but quantitative weights carry unquantified uncertainty.
  • domain assumption A 12x6 unit-cell cluster with periodic boundary conditions is large enough to capture the dimensional reduction, and the plotted path includes variation along both q_x and q_y.
    The cluster is elongated along the chains to favor quasi-1D behavior; only 6 unit cells span the interchain direction, limiting the resolution of the y-dispersion.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet." pith.science (2026). https://pith.science/paper/MBPVCV44

@misc{pith2026260804096,
  author       = {Pith},
  title        = {Pith review of: Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MBPVCV44}},
  note         = {Machine review of arXiv:2608.04096}
}
abstract

Low dimensionality enhances quantum fluctuations, triggering novel states of quantum matter to emerge. In real materials, low dimensionality usually arises from spatially strongly anisotropic couplings. Here, we demonstrate a different mechanism: in two-dimensional systems with coupled alternating ferromagnetic (FM) and antiferromagnetic (AFM) spin-$1/2$ chains, an applied magnetic field may drive a dimensional reduction. Under magnetic field, the FM chains polarize and stiffen, suppressing the propagation of transverse AFM fluctuations from one chain to another, and effectively induce one-dimensional behavior at low energies. For a model describing botallackite, Cu$_2$(OH)$_3$Br, quantum Monte Carlo dynamics show that beyond a critical magnetic field, the low-energy spectrum reduces to that of a one-dimensional AFM Heisenberg spin-$1/2$ chain with field-dependent incommensurate two-spinon fluctuations, providing clear signatures for inelastic neutron scattering.

Figures

Figures reproduced from arXiv: 2608.04096 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of the two-dimensional model for botal [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Static structure factor for various temperatures at zero magnetic field for a path [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Dynamical structure factors of the decoupled AFM chains [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Separate contributions from the FM and AFM chains to the dynamical structure factor at temperature [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Static structure factor of the AFM chains for a path [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Antiferromagnetic Heisenberg spin-1 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

74 extracted references · 68 canonical work pages

  1. [20]

    Heinze, T

    L. Heinze, T. Kotte, R. Rausch, A. Demuer, S. Luther, R. Fey- erherm, E. L. Q. N. Ammerlaan, U. Zeitler, D. I. Gorbunov, M. Uhlarz, K. C. Rule, A. U. B. Wolter, H. K¨ uhne, J. Wosnitza, 6 C. Karrasch, and S. S¨ ullow, Atacamite Cu 2Cl(OH) 3 in high magnetic fields: Quantum criticality and dimensional reduction of a sawtooth-chain compound, Phys. Rev. Lett...

    work page 2025

  2. [44]

    D. C. Dender, P. R. Hammar, D. H. Reich, C. Broholm, and G. Aeppli, Direct observation of field-induced incommensu- rate fluctuations in a one-dimensional𝑆=1/2 antiferromagnet, Phys. Rev. Lett.79, 1750 (1997)

    work page 1997

  3. [1]

    [10] [20] [21][22] 0 3 6 9 12ω(meV) (b) Sxy(q,ω)

    work page

  4. [2]

    [10] [20] [21][22] (c) Sxy(q,ω)

    work page

  5. [3]

    [10] [20] [21][22] (d) Sxy(q,ω) 10□2 10□1 100 101T = 3.074 K T = 6.148 K T = 12.296 K FIG. 2. (a) Static structure factor for various temperatures at zero magnetic field for a path(𝑞 𝑥,𝑞𝑦)=(0,𝜋)→(2𝜋,𝜋). (b)–(d): Dynamical structure factors for the same temperatures at zero magnetic field.𝒒=[00]corresponds to the total spin. Since this is a conserved quant...

    work page

  6. [4]

    With the exception of magnetic van der Waals materials [45]

    work page

  7. [5]

    In the vicinity of𝒒=[00], we observe a linearly dispersing spin- wave mode with a larger velocity, consistent with the linear spin-wave calculations [30]

    is very small (see the supplemental Material [30]). In the vicinity of𝒒=[00], we observe a linearly dispersing spin- wave mode with a larger velocity, consistent with the linear spin-wave calculations [30]. These gapless modes at [00] and

    work page

  8. [6]

    A standard route to dimensional reduction is through ther- mal fluctuations

    are associated with the spontaneous SU(2) spin-rotation symmetry breaking in the ordered ground state. A standard route to dimensional reduction is through ther- mal fluctuations. As the temperature rises, thermal fluctua- tions first overcome the weak interchain coupling scale, sup- pressing interchain correlations, while intrachain correlations associat...

    work page

Show all 74 references
  1. [7]

    [10] [20] [30] 0 3 6 9 12ω(meV) (a) SAFMxy (q,ω)

  2. [8]

    [10] [20] [30] (b) SAFMz (q,ω) 10□2 10□1 100 101 FIG. 3. Dynamical structure factors of the decoupled AFM chains (i.e.,𝐽 3 =0)at temperature𝑇=3.074 K and magnetic field𝐵= 36.625 T. Since𝑆 𝑧 tot is a conserved quantity, we leave [00] blank similar to Fig. 2. becomes strongly su...

  3. [9]

    [10] [20] [21][22] 0 3 6 9 12ω(meV) (m) SFMz (q,ω)

  4. [10]

    [10] [20] [21][22] (n) SFMz (q,ω)

  5. [11]

    [10] [20] [21][22] (o) SFMz (q,ω)

  6. [12]

    IN 0082025 SK

    [10] [20] [21][22] (p) SFMz (q,ω) 10□2 10□1 100 101 B = 10.987 T B = 21.975 T B = 45.781 T B = 64.093 T FIG. 4. Separate contributions from the FM and AFM chains to the dynamical structure factor at temperature𝑇=3.074K for various magnetic fields. We leave [00] blank in (o) an...

  7. [13]

    Bethe, Zur theorie der metalle, Zeitschrift f¨ ur Physik71, 205 (1931)

    H. Bethe, Zur theorie der metalle, Zeitschrift f¨ ur Physik71, 205 (1931)

    1931

  8. [14]

    Giamarchi,Quantum physics in one dimension(Clarendon Press, Oxford, 2004)

    T. Giamarchi,Quantum physics in one dimension(Clarendon Press, Oxford, 2004)

    2004

  9. [15]

    Kitaev, Anyons in an exactly solved model and beyond, An- nals of Physics321, 2 (2006)

    A. Kitaev, Anyons in an exactly solved model and beyond, An- nals of Physics321, 2 (2006)

    2006

  10. [16]

    A. A. Kulbakov, D. Y. Kononenko, S. Nishimoto, Q. Stahl, A. M. Chakkingal, M. Feig, R. Gumeniuk, Y. Skourski, L. Bhaskaran, S. A. Zvyagin, J. P. Embs, I. Puente-Orench, A. Wildes, J. Geck, O. Janson, D. S. Inosov, and D. C. Peets, Coupled frustrated ferromagnetic and antiferro...

    2022

  11. [17]

    C. D. Batista, J. Schmalian, N. Kawashima, P. Sengupta, S. E. Sebastian, N. Harrison, M. Jaime, and I. R. Fisher, Geomet- ric frustration and dimensional reduction at a quantum critical point, Phys. Rev. Lett.98, 257201 (2007)

    2007

  12. [18]

    S. E. Sebastian, N. Harrison, C. D. Batista, L. Balicas, M. Jaime, P. A. Sharma, N. Kawashima, and I. R. Fisher, Dimensional reduction at a quantum critical point, Nature441, 617 (2006)

    2006

  13. [19]

    R ¨osch and M

    O. R ¨osch and M. Vojta, Quantum phase transitions and dimen- sional reduction in antiferromagnets with interlayer frustration, Phys. Rev. B76, 180401(R) (2007)

    2007

  14. [21]

    This can be seen from the presence of the Bragg peaks in the static structure factor at low temperatures, as shown in Fig

    ≡ (2𝜋,𝜋), corresponding to the FM and AFM chains ordered antiferromagnetically along theˆ𝒚direction, respec- tively. This can be seen from the presence of the Bragg peaks in the static structure factor at low temperatures, as shown in Fig. 2(a). Total dynamical structure facto...

  15. [22]

    Martin, M

    S. Martin, M. Raczkowski, F. F. Assaad, and T. Grover, Dimensionality-changing transition from a non-fermi liquid to a spin-solid in a multichannel kondo lattice, arXiv:2510.19937 (2025), arXiv:2510.19937 [cond-mat.str-el]

    2025

  16. [23]

    S. E. Nagler, D. A. Tennant, R. A. Cowley, T. G. Perring, and S. K. Satija, Spin dynamics in the quantum antiferromagnetic chain compound KCuF3, Phys. Rev. B44, 12361 (1991)

    1991

  17. [24]

    D. A. Tennant, T. G. Perring, R. A. Cowley, and S. E. Nagler, Un- bound spinons in the𝑆=1/2 antiferromagnetic chain KCuF 3, Phys. Rev. Lett.70, 4003 (1993)

    1993

  18. [25]

    B. Lake, D. A. Tennant, J.-S. Caux, T. Barthel, U. Schollw ¨ock, S. E. Nagler, and C. D. Frost, Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain, Phys. Rev. Lett.111, 137205 (2013)

    2013

  19. [26]

    Zheludev, M

    A. Zheludev, M. Kenzelmann, S. Raymond, E. Ressouche, T. Masuda, K. Kakurai, S. Maslov, I. Tsukada, K. Uchinokura, and A. Wildes, Energy separation of single-particle and contin- uum states in anS=1/2 weakly coupled chains antiferromag- net, Phys. Rev. Lett.85, 4799 (2000)

    2000

  20. [27]

    Skoulatos, M

    M. Skoulatos, M. M˚ansson, C. Fiolka, K. W. Kr¨amer, J. Schefer, J. S. White, and C. R¨ uegg, Dimensional reduction by pressure in the magnetic framework material CuF 2(D2O)2(pyz): From spin-wave to spinon excitations, Phys. Rev. B96, 020414(R) (2017)

    2017

  21. [28]

    B. Lake, A. M. Tsvelik, S. Notbohm, D. Alan Tennant, T. G. Per- ring, M. Reehuis, C. Sekar, G. Krabbes, and B. Buchner, Con- finement of fractional quantum number particles in a condensed- matter system, Nature Phys.6, 50 (2010)

    2010

  22. [29]

    Reinold, L

    A. Reinold, L. Berger, M. Raczkowski, Z. Zhao, Y. Kohama, M. Gen, D. I. Gorbunov, Y. Skourski, S. Zherlitsyn, F. F. Assaad, T. Lorenz, and Z. Wang, Magnetization process of a quasi-two- dimensional quantum magnet: Two-step symmetry restoration and dimensional reduction, Phys. ...

    2025

  23. [30]

    Zhang, Z

    H. Zhang, Z. Zhao, D. Gautreau, M. Raczkowski, A. Saha, V. O. Garlea, H. Cao, T. Hong, H. O. Jeschke, S. D. Mahanti, T. Birol, F. F. Assaad, and X. Ke, Coexistence and interaction of spinons and magnons in an antiferromagnet with alternating antiferromagnetic and ferromagnetic...

    2020

  24. [31]

    D. M. Gautreau, A. Saha, and T. Birol, First-principles char- acterization of the magnetic properties of Cu 2(OH)3Br, Phys. Rev. Mater.5, 024407 (2021)

    2021

  25. [32]

    K. Y. Povarov, Y. Skourskii, J. Wosnitza, D. E. Graf, Z. Zhao, and S. A. Zvyagin, High-field magnetic properties of the alter- nating ferromagnetic-antiferromagnetic spin-chain compound Cu2(OH)3Br, Phys. Rev. B110, 214421 (2024)

    2024

  26. [33]

    Z. Y. Zhao, H. L. Che, R. Chen, J. F. Wang, X. F. Sun, and Z. Z. He, Magnetism study on a triangular lattice antiferromagnet Cu2(OH)3Br, Journal of Physics: Condensed Matter31, 275801 (2019)

    2019

  27. [34]

    F. F. Assaad, M. Bercx, F. Goth, A. G¨otz, J. S. Hofmann, E. Huff- man, Z. Liu, F. P. Toldin, J. S. E. Portela, and J. Schwab, The ALF (Algorithms for Lattice Fermions) project release 2.4. Doc- umentation for the auxiliary-field quantum Monte Carlo code, SciPost Phys. Codebas...

    2025

  28. [35]

    Blankenbecler, D

    R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Monte carlo calculations of coupled boson-fermion systems., Phys. Rev. D 24, 2278 (1981)

    1981

  29. [36]

    White, D

    S. White, D. Scalapino, R. Sugar, E. Loh, J. Gubernatis, and R. Scalettar, Numerical study of the two-dimensional hubbard model, Phys. Rev. B40, 506 (1989)

    1989

  30. [37]

    Assaad and H

    F. Assaad and H. Evertz, World-line and determinantal quantum Monte Carlo methods for spins, phonons and electrons, inCom- putational Many-Particle Physics, Lecture Notes in Physics, Vol. 739, edited by H. Fehske, R. Schneider, and A. Weiße (Springer, Berlin Heidelberg, 2008) ...

    2008

  31. [38]

    Sato and F

    T. Sato and F. F. Assaad, Quantum Monte Carlo simulation of generalized Kitaev models, Phys. Rev. B104, L081106 (2021)

    2021

  32. [39]

    Sandvik, Stochastic method for analytic continuation of quan- tum Monte Carlo data, Phys

    A. Sandvik, Stochastic method for analytic continuation of quan- tum Monte Carlo data, Phys. Rev. B57, 10287 (1998)

    1998

  33. [40]

    K. S. D. Beach, Identifying the maximum entropy method as a special limit of stochastic analytic continuation, arXiv e-prints 10.48550/arXiv.cond-mat/0403055 (2004)

    2004 doi arXiv

  34. [41]

    Shao and A

    H. Shao and A. W. Sandvik, Progress on stochastic analytic continuation of quantum Monte Carlo data, Physics Reports 1003, 1 (2023)

    2023

  35. [42]

    It also includes Refs

    See the Supplemental Material at [URL will be provided by the publisher] for details of the linear spin-wave analysis and the quantum Monte Carlo simulations. It also includes Refs. [22, 46– 49]

  36. [43]

    M¨ uller, H

    G. M¨ uller, H. Thomas, H. Beck, and J. C. Bonner, Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field, Phys. Rev. B24, 1429 (1981)

    1981

  37. [45]

    M. B. Stone, D. H. Reich, C. Broholm, K. Lefmann, C. Rischel, C. P. Landee, and M. M. Turnbull, Extended quantum critical phase in a magnetized spin- 1 2 antiferromagnetic chain, Phys. Rev. Lett.91, 037205 (2003)

    2003

  38. [46]

    Matsuda, H

    M. Matsuda, H. Onishi, A. Okutani, J. Ma, H. Agrawal, T. Hong, D. M. Pajerowski, J. R. D. Copley, K. Okunishi, M. Mori, S. Kimura, and M. Hagiwara, Magnetic structure and dispersion relation of the𝑆= 1 2 quasi-one-dimensional Ising-like antifer- romagnet BaCo2V2O8 in a transve...

    2017

  39. [47]

    Faure, S

    Q. Faure, S. Takayoshi, V. Simonet, B. Grenier, M. M ˚ansson, J. S. White, G. S. Tucker, C. R¨ uegg, P. Lejay, T. Giamarchi, and S. Petit, Tomonaga-Luttinger liquid spin dynamics in the quasi-one-dimensional Ising-like antiferromagnet BaCo2V2O8, Phys. Rev. Lett.123, 027204 (2019)

    2019

  40. [48]

    Grossjohann and W

    S. Grossjohann and W. Brenig, Spin dynamics of the antiferro- magnetic spin- 1 2 chain at finite magnetic fields and intermediate temperatures, Phys. Rev. B79, 094409 (2009)

    2009

  41. [49]

    Kohno, Dynamically dominant excitations of string solu- tions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field, Phys

    M. Kohno, Dynamically dominant excitations of string solu- tions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field, Phys. Rev. Lett.102, 037203 (2009)

    2009

  42. [50]

    Affleck and J

    I. Affleck and J. B. Marston, Large-nlimit of the Heisenberg- Hubbard model: Implications for high-𝑇 𝑐 superconductors, Phys. Rev. B37, 3774 (1988)

    1988

  43. [51]

    A. B. Zamolodchikov, Integrals of motion and𝑆-matrix of the (scaled)𝑇=𝑇 𝑐 Ising model with magnetic field, International Journal of Modern Physics A04, 4235 (1989)

    1989

  44. [52]

    Coldea, D

    R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, Quantum criticality in an Ising chain: Experimental 7 evidence for emergent𝐸 8 symmetry, Science327, 177 (2010)

    2010

  45. [53]

    Zhang, K

    Z. Zhang, K. Amelin, X. Wang, H. Zou, J. Yang, U. Nagel, T. R˜o om, T. Dey, A. A. Nugroho, T. Lorenz, J. Wu, and Z. Wang, Observation of𝐸 8 particles in an Ising chain antiferromagnet, Phys. Rev. B101, 220411(R) (2020)

    2020

  46. [54]

    Amelin, J

    K. Amelin, J. Engelmayer, J. Viirok, U. Nagel, T. R ˜o om, T. Lorenz, and Z. Wang, Experimental observation of quan- tum many-body excitations of𝐸 8 symmetry in the Ising chain ferromagnet CoNb2O6, Phys. Rev. B102, 104431 (2020)

    2020

  47. [55]

    Amelin, J

    K. Amelin, J. Viirok, U. Nagel, T. R˜o˜om, J. Engelmayer, T. Dey, A. Agung Nugroho, T. Lorenz, and Z. Wang, Quantum spin dynamics of quasi-one-dimensional Heisenberg-Ising magnets in a transverse field: confined spinons,𝐸 8 spectrum, and quan- tum phase transitions, Journal of...

    2022

  48. [56]

    Reinold, L

    A. Reinold, L. Peedu, K. Amelin, U. Nagel, T. R˜o˜om, S. Luther, H. K¨ uhne, D. Wulferding, K. Mukhuti, M. W. de Dreu, P. C. M. Christianen, D. Kudlacik, D. Yakovlev, Z. Zhao, T. Nakajima, Y. Kohama, T. Lorenz, F. Lisandrini, C. Kollath, M. Raczkowski, F. F. Assaad, and Z. Wan...

    2026 arXiv

  49. [57]

    K. S. Burch, D. Mandrus, and J.-G. Park, Magnetism in two- dimensional van der Waals materials, Nature563, 47 (2018)

    2018

  50. [59]

    Holstein and H

    T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev.58, 1098 (1940)

    1940

  51. [60]

    Auerbach,Interacting electrons and quantum magnetism., Graduate texts in contemporary physics (Springer, New York, Berlin, Heidelberg, 1994)

    A. Auerbach,Interacting electrons and quantum magnetism., Graduate texts in contemporary physics (Springer, New York, Berlin, Heidelberg, 1994)

    1994

  52. [61]

    Colpa, Diagonalization of the quadratic boson Hamiltonian, Physica A: Statistical Mechanics and its Applications93, 327 (1978)

    J. Colpa, Diagonalization of the quadratic boson Hamiltonian, Physica A: Statistical Mechanics and its Applications93, 327 (1978)

    1978

  53. [62]

    Magnetic-Field-Driven Dimensional Reduction in a Quantum Antiferromagnet

    M. Raczkowski and F. F. Assaad, Spinon confinement: Dynam- ics of weakly coupled Hubbard chains, Phys. Rev. B88, 085120 (2013). END MATTER A. Parton Mean-Field Theory of the Incommensurate Spinon Excitations in the Heisenberg Antiferromagnetic Spin-1/2Chain We adopt the Abriko...

    2013

  54. [63]

    [10] [20] [21] [22] 0 2 4 6ω(meV) (b) B = 20 T FIG. S2. Linear spin-wave spectra at magnetic fields (a)𝐵= 0 T and (b)𝐵= 20 T. where 𝒓 and 𝒓′ label the unit cells, 𝑱𝒓−𝒓′, 𝛼𝛽 is a 3× 3 matrix encoding the exchange interactions between the𝛼th and𝛽th orbitals connected by the vect...

  55. [64]

    [10] [20] [21] [22] 0 2 4 6ω(meV) B = 20 T Sz(q,ω)(c) 10□3 10□2 10□1 100 101 102 103 FIG. S3. Dynamical structure factors obtained from linear spin-wave theory at 𝑇 = 0 K. (a) dynamical structure factor at zero magnetic field. (b) Transverse and (c) longitudinal dynamical stru...

  56. [69]

    [10] [20][21][22] (t) Sz(q,ω) B = 73.25 T 10□2 10□1 100 101 FIG. S4. Transverse and longitudinal components of the total dynamical structure factor at temperature 𝑇 = 3.074 K for various magnetic fields. Since 𝑆𝑧 tot is a conserved quantity, the longitudinal structure factorS𝑧...

  57. [70]

    [10] [20][21][22] 0 3 6 9 12ω(meV) (p)Sz(q,ω) B = 36.625 T

  58. [71]

    [10] [20][21][22] (q)Sz(q,ω) B = 45.781 T

  59. [72]

    [10] [20][21][22] (r) Sz(q,ω) B = 54.938 T

  60. [73]

    [10] [20][21][22] (s) Sz(q,ω) B = 64.094 T

  61. [74]

    [10] [20][21][22] (t) Sz(q,ω) B = 73.25 T 10□2 10□1 100 101 FIG. S5. Transverse and longitudinal components of the total dynamical structure factor at temperature 𝑇 = 6.148 K for various magnetic fields. Since 𝑆𝑧 tot is a conserved quantity, we leave [00] blank in all panels o...

  62. [75]

    Khatua, G

    S. Khatua, G. C. Howson, M. J. P. Gingras, and J. G. Rau, Ground state properties of the Heisenberg-compass model on the square lattice, Phys. Rev. B110, 104426 (2024)

    2024

  63. [76]

    Holstein and H

    T. Holstein and H. Primakoff, Field dependence of the intrinsic domain magnetization of a ferromagnet, Phys. Rev. 58, 1098 (1940)

    1940

  64. [77]

    Auerbach, Interacting electrons and quantum magnetism

    A. Auerbach, Interacting electrons and quantum magnetism. , Graduate texts in contemporary physics (Springer, New York, Berlin, Heidelberg, 1994)

    1994

  65. [78]

    Colpa, Diagonalization of the quadratic boson Hamiltonian, Physica A: Statistical Mechanics and its Applications 93, 327 (1978)

    J. Colpa, Diagonalization of the quadratic boson Hamiltonian, Physica A: Statistical Mechanics and its Applications 93, 327 (1978)

    1978

  66. [79]

    F. F. Assaad, M. Bercx, F. Goth, A. G ¨otz, J. S. Hofmann, E. Huffman, Z. Liu, F. P. Toldin, J. S. E. Portela, and J. Schwab, The ALF (Algorithms for Lattice Fermions) project release 2.4. Documentation for the auxiliary-field quantum Monte Carlo code, SciPost Phys. Codebases ...

    2025

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.