Pith. sign in

REVIEW 2 major objections 5 minor 1 cited by

From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The Shastry-Sutherland pVBS–Néel transition is weak first order, and a tricritical point appears on the route to the J1-J2 model.

desk verdict Strong new numerics resolve the pure Shastry-Sutherland transition as weak first-order; the tri-critical point is a plausible but unproven inference from a null result. read the letter →

arxiv 2411.17452 v1 pith:6Y6M2OJN submitted 2024-11-26 cond-mat.str-el quant-ph

Xiangjian Qian , Rongyi Lv , Jong Yeon Lee , Mingpu Qin This is my paper · ORCID
classification cond-mat.str-elquant-ph
keywords Shastry-SutherlandmodelJ1-J2HeisenbergplaquettevalencebondstateNéelantiferromagnetweakfirst-ordertransitiontricriticalpointdeconfinedquantumcriticalfullyaugmentedmatrixproduct
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

The paper proposes a one-parameter family of spin models that interpolates between the Shastry-Sutherland model and the J1-J2 Heisenberg model, and uses it to settle the nature of the transition between the plaquette valence bond state (pVBS) and the Néel antiferromagnetic (AFM) phases. In the pure Shastry-Sutherland model, the authors find this transition is a weak first-order transition at α = J1/J3 = 0.785(5). In the interpolating model, the transition remains direct for every value studied, but changes from first-order to continuous as the J1-J2 limit is approached, placing a tricritical point at Δ = J3 − J3′ between roughly 0.2 and 0.3. A sympathetic reader cares because this identifies where the much-studied deconfined-quantum-critical-point scenario would have to live: not at the pure Shastry-Sutherland transition, but at a nearby multicritical point, and because the family provides a concrete tunable platform for probing that physics.

What carries the argument

The central object is the generalized Shastry-Sutherland Hamiltonian H = J1 Σ⟨i,j⟩ Si·Sj + J3 Σblue Si·Sj + J3′ Σred Si·Sj, in which the next-nearest-neighbor bonds are split into blue and red sets so that J3′ = 0 recovers the Shastry-Sutherland model and J3′ = J3 recovers the J1-J2 Heisenberg model. The argument runs on three probes: the AFM correlation ratio ξm/L, the crossing of the lowest singlet and triplet gaps, and the first derivative of the ground-state energy with respect to the tuning parameter, evaluated by the Feynman–Hellmann theorem. The energy derivative is the decisive instrument: a finite-size crossing that persists and shifts toward the phase boundary as L grows is the numerical signature of a first-order transition, while its absence signals continuity. Large-scale density matrix renormalization group and fully augmented matrix product state calculations reach cylinder circumferences up to L = 16 with truncation errors near or below 1×10−5, and all reported quantities are extrapolated to zero truncation error.

What would settle it

Repeat the ∂e/∂β calculation at Δ = 0.2 on cylinders with circumference L = 18 and L = 20. If a crossing in ∂e/∂β reappears at finite L and shifts exponentially slowly toward the transition point as L grows, the transition is still first-order at Δ = 0.2, contradicting the paper's placement of the tricritical point; if the curves remain nested and crossing-free, the paper's conclusion is supported. A complementary check is a direct thermodynamic measurement of latent heat—a discontinuity in ∂e/∂β in the infinite-size limit—at Δ = 0.2.

Watch

Extended reading notes

Core claim

On the paper's own terms: in the pure Shastry-Sutherland model, the phase boundary between the plaquette valence bond state and the Néel antiferromagnet is a direct, weak first-order transition at α = 0.785(5), established by agreement among the AFM correlation-ratio crossing, singlet–triplet gap crossing, pVBS order parameters, and a crossing in ∂e/∂α obtained from the Feynman–Hellmann theorem. In the generalized model with J3 = J3′ + Δ, the same transition remains direct for all Δ studied, but the energy-derivative crossing that signals first-order behavior disappears as Δ decreases: it is present at Δ = 0.6 and Δ = 0.4, weakens at Δ = 0.3, and is absent at Δ = 0.2. The authors conclude that the order of the transition changes between Δ = 0.2 and Δ = 0.3, and that this tricritical point is where the continuous transition of the J1-J2 model connects to the first-order Shastry-Sutherland transition.

Load-bearing premise

The load-bearing premise is that the absence of a crossing in ∂e/∂β at Δ = 0.2 for system sizes up to L = 16 indicates a genuinely continuous transition; because weak first-order transitions shift exponentially with system size, a very weak first-order transition could still hide below the accessible sizes, a possibility the paper itself concedes when it says a 'very narrow intermediate region' cannot be ruled out.

Editorial extensions

If this is right

  • In the pure Shastry-Sutherland model, the pVBS–Néel transition is not a deconfined quantum critical point; it is a weak first-order transition with phase coexistence signaled by the crossing in ∂e/∂α.
  • There is no intervening spin-liquid phase along the pVBS–Néel boundary in either limit or in the interpolated model, at least within the numerical resolution of the study.
  • The transition between the pVBS and Néel phases turns continuous somewhere between Δ = 0.3 and Δ = 0.2, so the J1-J2 Heisenberg limit lies on the continuous side of a tricritical point.
  • The generalized model offers a tunable microscopic Hamiltonian in which the crossover from first-order to continuous quantum criticality, including the deconfined-criticality scenario, can be studied directly.
  • If the generalized model is a more realistic description of materials such as SrCu2(BO3)2, the weak first-order character of the pure-model transition should be visible as a small latent-heat-like feature in high-precision measurements tuned across the phase boundary.

Reading between the lines

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

  • If the tricritical point is real, a field-theoretic description of a tricritical deconfined quantum critical point—possibly with emergent SO(5) symmetry along the lines sketched in the paper's reference for multicriticality—should control the crossover; that theory is not developed in this paper.
  • The bracketed location 'between Δ = 0.2 and Δ = 0.3' is based on the absence of a crossing at Δ = 0.2 for L up to 16; because weak first-order crossings shift exponentially in system size, the true tricritical point could lie below Δ = 0.2, so a dedicated higher-size search at Δ = 0.2 would sharpen the estimate.
  • A natural experimental extension is to tune the 'red' diagonal bonds in SrCu2(BO3)2 via pressure or chemical substitution, effectively moving the material along this interpolation and searching for the predicted change in the order of the transition.
  • The same energy-derivative crossing diagnostic could be applied to other frustrated magnets where the debate between weak first-order and continuous quantum transitions remains unresolved.
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

2 major / 5 minor

Summary. The paper proposes a generalized Shastry-Sutherland (SS) model that interpolates continuously between the SS model and the square-lattice J1-J2 Heisenberg model, and studies the plaquette valence bond (pVBS) to Néel antiferromagnet (AFM) transition using large-scale DMRG and fully augmented matrix product states on cylinders up to width 16, with truncation-error extrapolation. The authors report that in the pure SS model the pVBS-AFM transition is a weak first-order transition at alpha = J1/J3 = 0.785(5), supported by agreement among correlation-ratio crossings, singlet-triplet gap crossings, and a crossing of d e/d alpha. In the generalized model, they report that the first-order transition persists for Delta = J3 - J3' >= 0.4 but the energy-derivative crossing disappears for Delta = 0.3 and 0.2, leading them to locate a tri-critical point at which the transition becomes continuous, somewhere between Delta = 0.2 and 0.3, connecting to a previously claimed continuous transition in the J1-J2 limit.

Significance. If correct, the pure-SS result settles a long-standing controversy and aligns with recent proposals of a proximate deconfined critical point in SrCu2(BO3)2. The generalized model provides a new platform for studying the evolution of quantum criticality, and the tri-critical point is of intrinsic theoretical interest. The numerics are state of the art: bond dimensions up to 60000 U(1) states, explicit truncation-error extrapolation, agreement with exact diagonalization for a 6x6 system, and consistency among several independent finite-size estimators. The main caveat is that the continuous branch is inferred from the absence of a crossing in d e/d beta, which is not a positive signature; this limits the strength of the tri-critical-point claim.

major comments (2)
  1. [Bridging the Shastry-Sutherland Model to the J1-J2 Heisenberg Model; Fig. 4] The inference that the transition becomes continuous for small Delta rests on the absence of a crossing in d e/d beta for Delta = 0.2 and 0.3 (Fig. 4(c,d)). For a first-order transition, the finite-size crossing point approaches the transition point with a deviation bounded by O(e^{-L}) (Ref. [55]); consequently, a weak first-order transition with a small jump in the derivative operator can produce exactly the observed behavior at L <= 16, where inter-L differences are of order 0.005-0.01 (inset of Fig. 4(d)). The absence of an observed crossing is a null result, not a positive signature of continuity. Because the same null criterion underlies the continuous-transition claim for the J1-J2 limit (Ref. [43]), the existence and approximate location of the tri-critical point are not yet established by the data. I recommend either providing a positive finite-size scaling signature of the continuous transition (e.g., critical exponent extraction or scaling collapse) or explicitly downgrading the tri-critical point statement to a conjecture consistent with the data.
  2. [Bridging the Shastry-Sutherland Model to the J1-J2 Heisenberg Model; Fig. 1(c)] The reported location of the tri-critical point ('between Delta = 0.2 and Delta = 0.3') is given without an uncertainty estimate and without a quantitative bound on a possible small first-order jump along that branch. Since the data at Delta = 0.3 and 0.2 are only consistent with the absence of a crossing, and since the J1-J2 limit is taken from Ref. [43] rather than computed here, the actual onset of continuity could occur anywhere in this interval. A systematic error estimate, or an estimate of the jump size via a Maxwell construction, is needed to make the phase-diagram claim quantitative.
minor comments (5)
  1. [Title and abstract] The title 'From the Shastry-Sutherland model to theJ1-J2 Heisenberg model' has a missing space between 'the' and 'J1-J2'.
  2. [Abstract] The abstract uses 'PVBS' while the rest of the paper uses 'pVBS'; please standardize the notation.
  3. [Fig. 4 caption] In the caption of Fig. 4, 'To show the crossing points clearer' should read 'more clearly'.
  4. [Supplementary Materials] In the supplementary, the equation for O2 in Appendix B is numbered (S1), duplicating the equation number for the AFM order parameter in Appendix A; please renumber the equations.
  5. [Introduction] The phrase 'The SS model contains rich phases' is informal; consider 'The SS model hosts a rich phase diagram'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central pVBS-to-AFM results are new DMRG/FAMPS simulations, and the tri-critical inference rests on an observed change in the energy-derivative signal rather than on a fitted parameter or a self-referential definition.

full rationale

The paper derives its two main claims from new numerical data for explicit spin Hamiltonians. The pure Shastry-Sutherland pVBS-to-AFM transition is characterized by three independent finite-size diagnostics -- the AFM correlation-ratio crossing, the S=0/S=1 gap crossing, and the Feynman-Hellmann derivative ∂e/∂α crossing -- which all extrapolate to the same α=0.785(5); no parameter is fitted to one subset and then promoted to a prediction of a closely related quantity. The existence and location of the tri-critical point are inferred from a direct comparison across the interpolation parameter Δ: for Δ=0.6 and Δ=0.4 the ∂e/∂β curves show a first-order crossing, while for Δ=0.3 and Δ=0.2 the crossing is absent, with the phase boundary itself tracked by correlation-ratio and gap crossings. The continuous character of the J1-J2 endpoint is taken from the authors' prior work (Ref. [43]), and the pVBS identification from Ref. [41], but these are published external calculations rather than parameters fitted in this paper, and the new Δ=0.3 and Δ=0.2 data do not reduce to those citations. The paper explicitly acknowledges that a 'very narrow intermediate region' cannot be ruled out numerically, and the finite-size behavior of weak first-order transitions (O(e^{-L})) means the disappearance of a crossing at L≤16 could in principle be a weak first-order signal; however, this is a statistical-falsifiability limitation, not a case where a prediction is equivalent to its input by construction. No circular step can be exhibited.

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

The central claim rests on numerical DMRG/F-AMPS simulations of a specific spin Hamiltonian. No fitting parameters are introduced beyond the Hamiltonian couplings themselves. The main inference about continuity near the J1-J2 limit depends on the prior result in Ref. [43] and on the interpretation of the absence of a crossing in the energy derivative.

assumptions (4)
  • domain assumption The generalized Hamiltonian Eq. (3) with J3 = J3' + Δ captures the relevant low-energy physics of both the SS and J1-J2 limits.
    The model is introduced as a bridge between the two limits; whether it is the most physical or representative interpolation is assumed, not derived.
  • domain assumption The Borgs-Kotecky finite-size scaling for first-order transitions (exponential approach of the derivative crossing point) applies to these cylinder geometries.
    This is used to interpret the ∂e/∂α crossing as a first-order signature in the SS model; the applicability to open-boundary cylinders is assumed.
  • domain assumption The J1-J2 Heisenberg model transition between pVBS and Néel is continuous, as reported in Ref. [43] by the same group.
    This prior result is the anchor for the continuous side of the tri-critical point; it is cited but not re-derived in this work.
  • standard math The Feynman-Hellmann theorem gives the energy derivative as an expectation value of a local operator.
    Used to compute ∂e/∂α and ∂e/∂β; this is a standard and unproblematic result.

how reviews work

0 comments
Cite this review

Pith. "Pith review of From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model." pith.science (2026). https://pith.science/paper/6Y6M2OJN

@misc{pith2026241117452,
  author       = {Pith},
  title        = {Pith review of: From the Shastry-Sutherland model to the $J_1$-$J_2$ Heisenberg model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6Y6M2OJN}},
  note         = {Machine review of arXiv:2411.17452}
}
abstract

We propose a generalized Shastry-Sutherland model which bridges the Shastry-Sutherland model and the $J_1$-$J_2$ Heisenberg model. By employing large scale Density Matrix Renormalization Group and Fully Augmented Matrix Product State calculations, combined with careful finite-size scaling, we find the phase transition between the plaquette valence bond state (PVBS) and Neel anti-ferromagnetic (AFM) phase in the pure Shastry-Sutherland model is a weak first one. This result indicates the existence of an exotic tri-critical point in the PVBS to AFM transition line in the phase diagram, as the transition in the $J_1$-$J_2$ Heisenberg model was previously determined to be continuous. We determine the location of the tri-critical point in the phase diagram at which first-order transition turns to continuous. Our generalized Shastry-Sutherland model provides not only a valuable platform to explore exotic phases and phase transitions but also more realistic description of Shastry-Sutherland materials like SrCu$_2$(BO$_3$)$_2$.

Figures

Figures reproduced from arXiv: 2411.17452 by the authors.

Figure 1
Figure 1. (a)) with circumferences up to L = 16. Unless oth￾erwise specified, we concentrate on L × 2L cylinder sys￾tems following [22]. For L ≤ 14, we present simulation results without disentanglers, i.e., employing the regular SU(2)-symmetric DMRG, and we push the bond dimen￾sion D up to 15000 SU(2) multiples, equivalent to about 60000 U(1) states to ensure high simulation accuracy. For L = 16, we employ the FAMPS method a… view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 1
Figure 1. Figure 1: sign-problem-free J-Q model was studied along a specific line cut exhibiting a first-order transition [59, 60]. Our comprehensive numerical investigation using a concrete model raises intriguing questions about the field-theoretic description of this transition. While …

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Accurate computation of the energy variance and $\langle\langle \mathcal{L}^\dagger \mathcal{L} \rangle\rangle$ using iPEPS

    cond-mat.str-el 2025-11 conditional novelty 6.0 of 10

    A large-cell CTMRG algorithm computes iPEPS energy variances accurately and efficiently, enabling zero-variance energy extrapolation and a steady-state quality measure for open quantum systems.

Reference graph

Works this paper leans on

74 extracted references · 46 canonical work pages · cited by 1 Pith paper

  1. [55]

    Borgs and R

    C. Borgs and R. Koteck´ y, A rigorous theory of finite- size scaling at first-order phase transitions, Journal of Statistical Physics 61, 79 (1990)

    work page 1990

  2. [43]

    Qian and M

    X. Qian and M. Qin, Absence of spin liquid phase in the J1 − J2 heisenberg model on the square lattice, Phys. Rev. B 109, L161103 (2024)

    work page 2024

  3. [1]

    Y. Cui, L. Liu, H. Lin, K.-H. Wu, W. Hong, X. Liu, C. Li, Z. Hu, N. Xi, S. Li, R. Yu, A. W. Sandvik, and W. Yu, Proximate deconfined quantum critical point in srcu2(bo3)2, Science 380, 1179 (2023)

    work page 2023

  4. [2]

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

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

    2010

  5. [3]

    Savary and L

    L. Savary and L. Balents, Quantum spin liquids: a re- view, Reports on Progress in Physics 80, 016502 (2016)

    2016

  6. [4]

    Senthil, A

    T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Deconfined quantum critical points, Sci- ence 303, 1490 (2004)

    2004

  7. [5]

    Senthil, Deconfined quantum critical points: a review, arXiv (2023), 2306.12638 [cond-mat.str-el]

    T. Senthil, Deconfined quantum critical points: a review, arXiv (2023), 2306.12638 [cond-mat.str-el]

    arXiv 2023

  8. [6]

    Wilczek, Quantum mechanics of fractional-spin parti- cles, Phys

    F. Wilczek, Quantum mechanics of fractional-spin parti- cles, Phys. Rev. Lett. 49, 957 (1982)

    1982

Show all 74 references
  1. [7]

    B. I. Halperin, Statistics of quasiparticles and the hierar- chy of fractional quantized hall states, Phys. Rev. Lett. 52, 1583 (1984)

    1984

  2. [8]

    Arovas, J

    D. Arovas, J. R. Schrieffer, and F. Wilczek, Fractional statistics and the quantum hall effect, Phys. Rev. Lett. 53, 722 (1984)

    1984

  3. [9]

    C. Han, Z. Iftikhar, Y. Kleeorin, A. Anthore, F. Pierre, Y. Meir, A. K. Mitchell, and E. Sela, Fractional entropy of multichannel kondo systems from conductance-charge relations, Phys. Rev. Lett. 128, 146803 (2022)

    2022

  4. [10]

    Brooks, M

    M. Brooks, M. Lemeshko, D. Lundholm, and E. Yak- aboylu, Molecular impurities as a realization of anyons on the two-sphere, Phys. Rev. Lett. 126, 015301 (2021)

    2021

  5. [11]

    A. W. W. Ludwig, D. Poilblanc, S. Trebst, and M. Troyer, Two-dimensional quantum liquids from inter- acting non-abelian anyons, New Journal of Physics 13, 045014 (2011)

    2011

  6. [12]

    Nakano, Y

    H. Nakano, Y. Minami, and S.-i. Sasa, Long-range phase order in two dimensions under shear flow, Phys. Rev. Lett. 126, 160604 (2021)

    2021

  7. [13]

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

    2006

  8. [14]

    Jiang and S

    H.-C. Jiang and S. A. Kivelson, High temperature su- perconductivity in a lightly doped quantum spin liquid, Phys. Rev. Lett. 127, 097002 (2021)

    2021

  9. [15]

    Xu, C.-M

    H. Xu, C.-M. Chung, M. Qin, U. Schollw¨ ock, S. R. White, and S. Zhang, Coexistence of su- perconductivity with partially filled stripes in the hubbard model, Science 384, eadh7691 (2024), https://www.science.org/doi/pdf/10.1126/science.adh7691

    2024 doi

  10. [16]

    Sriram Shastry and B

    B. Sriram Shastry and B. Sutherland, Exact ground state of a quantum mechanical antiferromagnet, Physica B+C 108, 1069 (1981)

    1981

  11. [17]

    Kageyama, K

    H. Kageyama, K. Yoshimura, R. Stern, N. V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. P. Slichter, T. Goto, and Y. Ueda, Exact dimer ground state and quantized magnetization plateaus in the two-dimensional spin sys- tem srcu2(bo3)2, Phys. Rev. Lett. 82, 3168 (1999)

    1999

  12. [18]

    J. L. Jim´ enez, S. P. G. Crone, E. Fogh, M. E. Za- yed, R. Lortz, E. Pomjakushina, K. Conder, A. M. L¨ auchli, L. Weber, S. Wessel, A. Honecker, B. Normand, C. R¨ uegg, P. Corboz, H. M. Rønnow, and F. Mila, A quantum magnetic analogue to the critical point of wa- ter, Nature ...

    2021

  13. [19]

    Senthil, L

    T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Quantum criticality beyond the landau- ginzburg-wilson paradigm, Phys. Rev. B 70, 144407 (2004)

    2004

  14. [20]

    M. A. Metlitski and R. Thorngren, Intrinsic and emer- gent anomalies at deconfined critical points, Phys. Rev. B 98, 085140 (2018)

    2018

  15. [21]

    J. Y. Lee, Y.-Z. You, S. Sachdev, and A. Vishwanath, Sig- natures of a deconfined phase transition on the shastry- sutherland lattice: Applications to quantum critical SrCu2(BO3)2, Phys. Rev. X 9, 041037 (2019)

    2019

  16. [22]

    J. Yang, A. W. Sandvik, and L. Wang, Quantum crit- icality and spin liquid phase in the shastry-sutherland model, Phys. Rev. B 105, L060409 (2022)

    2022

  17. [23]

    N. Xi, H. Chen, Z. Y. Xie, and R. Yu, Plaquette valence bond solid to antiferromagnet transition and deconfined quantum critical point of the shastry-sutherland model, Phys. Rev. B 107, L220408 (2023)

    2023

  18. [24]

    Liu, X.-T

    W.-Y. Liu, X.-T. Zhang, Z. Wang, S.-S. Gong, W.-Q. Chen, and Z.-C. Gu, Quantum criticality with emergent symmetry in the extended shastry-sutherland model, Phys. Rev. Lett. 133, 026502 (2024)

    2024

  19. [25]

    Corboz and F

    P. Corboz and F. Mila, Tensor network study of the shastry-sutherland model in zero magnetic field, Phys. Rev. B 87, 115144 (2013)

    2013

  20. [26]

    J. Wang, H. Li, N. Xi, Y. Gao, Q.-B. Yan, W. Li, and G. Su, Plaquette singlet transition, magnetic barocaloric effect, and spin supersolidity in the shastry-sutherland model, Phys. Rev. Lett. 131, 116702 (2023)

    2023

  21. [27]

    H. Chen, G. Duan, C. Liu, Y. Cui, W. Yu, Z. Y. Xie, and R. Yu, Spin excitations of the Shastry-Sutherland model – altermagnetism and proximate deconfined quan- tum criticality, arXiv e-prints , arXiv:2411.00301 (2024), arXiv:2411.00301 [cond-mat.str-el]

    2024

  22. [28]

    Loris Viteritti, R

    L. Loris Viteritti, R. Rende, A. Parola, S. Goldt, and F. Becca, Transformer Wave Function for the Shastry-Sutherland Model: emergence of a Spin- Liquid Phase, arXiv e-prints , arXiv:2311.16889 (2023), 6 arXiv:2311.16889 [cond-mat.str-el]

    2023 arXiv

  23. [29]

    R. R. P. Singh and R. Narayanan, Dimer versus twist order in the j1-j2 model, Phys. Rev. Lett. 65, 1072 (1990)

    1990

  24. [30]

    Read and S

    N. Read and S. Sachdev, Large-n expansion for frustrated quantum antiferromagnets, Phys. Rev. Lett. 66, 1773 (1991)

    1991

  25. [31]

    R. R. P. Singh, Z. Weihong, C. J. Hamer, and J. Oit- maa, Dimer order with striped correlations in the J1−j2 heisenberg model, Phys. Rev. B 60, 7278 (1999)

    1999

  26. [32]

    Capriotti and S

    L. Capriotti and S. Sorella, Spontaneous plaquette dimer- ization in the j1 − −j2 heisenberg model, Phys. Rev. Lett. 84, 3173 (2000)

    2000

  27. [33]

    Mambrini, A

    M. Mambrini, A. L¨ auchli, D. Poilblanc, and F. Mila, Pla- quette valence-bond crystal in the frustrated heisenberg quantum antiferromagnet on the square lattice, Phys. Rev. B 74, 144422 (2006)

    2006

  28. [34]

    S.-S. Gong, W. Zhu, D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher, Plaquette ordered phase and quantum phase diagram in the spin- 1 2 J1−J2 square heisenberg model, Phys. Rev. Lett. 113, 027201 (2014)

    2014

  29. [35]

    Yu and Y.-J

    J.-F. Yu and Y.-J. Kao, Spin- 1 2 J1-J2 heisenberg antifer- romagnet on a square lattice: A plaquette renormalized tensor network study, Phys. Rev. B 85, 094407 (2012)

    2012

  30. [36]

    W.-J. Hu, F. Becca, A. Parola, and S. Sorella, Direct evidence for a gapless Z2 spin liquid by frustrating n´ eel antiferromagnetism, Phys. Rev. B 88, 060402 (2013)

    2013

  31. [37]

    Wang and A

    L. Wang and A. W. Sandvik, Critical level crossings and gapless spin liquid in the square-lattice spin-1 /2 J1−J2 heisenberg antiferromagnet, Phys. Rev. Lett.121, 107202 (2018)

    2018

  32. [38]

    Nomura and M

    Y. Nomura and M. Imada, Dirac-type nodal spin liq- uid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy, Phys. Rev. X 11, 031034 (2021)

    2021

  33. [39]

    Liu, S.-S

    W.-Y. Liu, S.-S. Gong, Y.-B. Li, D. Poilblanc, W.-Q. Chen, and Z.-C. Gu, Gapless quantum spin liquid and global phase diagram of the spin-1/2 j1-j2 square antifer- romagnetic heisenberg model, Science Bulletin 67, 1034 (2022)

    2022

  34. [40]

    Jiang, H

    H.-C. Jiang, H. Yao, and L. Balents, Spin liquid ground state of the spin- 1 2 square J1-J2 heisenberg model, Phys. Rev. B 86, 024424 (2012)

    2012

  35. [41]

    Huang, X

    J. Huang, X. Qian, and M. Qin, Plaquette-type valence bond solid state in the J1−J2 square-lattice heisenberg model, Phys. Rev. B 110, 195111 (2024)

    2024

  36. [42]

    [41] using an infinitesimal symmetry breaking field and a proper finite size scaling

    In the J1-J2 Heisenberg model, a rigorous analysis to pin down plaquette over columnar VBS has been performed in Ref. [41] using an infinitesimal symmetry breaking field and a proper finite size scaling

  37. [44]

    H.-Y. Lin, Y. Guo, R.-Q. He, Z. Y. Xie, and Z.-Y. Lu, Green’s function monte carlo combined with projected entangled pair state approach to the frustrated J1−J2 heisenberg model, Phys. Rev. B 109, 235133 (2024)

    2024

  38. [45]

    S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett.69, 2863 (1992)

    1992

  39. [46]

    Qian and M

    X. Qian and M. Qin, Augmenting density matrix renor- malization group with disentanglers, Chinese Physics Letters 40, 057102 (2023)

    2023

  40. [47]

    Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96 (2011), january 2011 Special Issue

    U. Schollw¨ ock, The density-matrix renormalization group in the age of matrix product states, Annals of Physics 326, 96 (2011), january 2011 Special Issue

    2011

  41. [48]

    Nomura, Correlation functions of the 2d sine-gordon model, Journal of Physics A: Mathematical and General 28, 5451 (1995)

    K. Nomura, Correlation functions of the 2d sine-gordon model, Journal of Physics A: Mathematical and General 28, 5451 (1995)

    1995

  42. [49]

    Okamoto and K

    K. Okamoto and K. Nomura, Fluid-dimer critical point in s = 12 antiferromagnetic heisenberg chain with next nearest neighbor interactions, Physics Letters A169, 433 (1992)

    1992

  43. [50]

    Suwa and S

    H. Suwa and S. Todo, Generalized moment method for gap estimation and quantum monte carlo level spec- troscopy, Phys. Rev. Lett. 115, 080601 (2015)

    2015

  44. [51]

    A. W. Sandvik, Computational Studies of Quantum Spin Systems, AIP Conference Proceedings 1297, 135 (2010)

    2010

  45. [52]

    H. Suwa, A. Sen, and A. W. Sandvik, Level spectroscopy in a two-dimensional quantum magnet: Linearly dispers- ing spinons at the deconfined quantum critical point, Phys. Rev. B 94, 144416 (2016)

    2016

  46. [53]

    m2 s(k) = 1 L4 P ij⟨Si · Sj⟩eik(i−j), i = (ix, iy) is the site position and the summation runs over the center L × L sites

  47. [54]

    R. K. Kaul, Spin nematics, valence-bond solids, and spin liquids in SO( n) quantum spin models on the triangular lattice, Phys. Rev. Lett. 115, 157202 (2015)

    2015

  48. [56]

    The summation runs over the center L × L sites

    Nb is the number of bonds in the calculation, qa is the wave vector associated with the VBS order, taking values (π, 0) or (0, π) depending on the direction a of the dimer order. The summation runs over the center L × L sites

  49. [57]

    Results for L × 2L systems, provided in the sup- plementary material, also exhibit a crossing point at the transition

    Here, we show the results for L × 2.5L systems, which reveal a more pronounced crossing point than L × 2L systems. Results for L × 2L systems, provided in the sup- plementary material, also exhibit a crossing point at the transition

  50. [58]

    Takahashi, H

    J. Takahashi, H. Shao, B. Zhao, W. Guo, and A. W. Sandvik, So(5) multicriticality in two-dimensional quan- tum magnets (2024), arXiv:2405.06607 [cond-mat.str-el]

    2024 arXiv

  51. [59]

    Takahashi and A

    J. Takahashi and A. W. Sandvik, Valence-bond solids, vestigial order, and emergent so(5) symmetry in a two- dimensional quantum magnet, Phys. Rev. Res. 2, 033459 (2020)

    2020

  52. [60]

    B. Zhao, P. Weinberg, and A. W. Sandvik, Symmetry- enhanced discontinuous phase transition in a two- dimensional quantum magnet, Nature Physics 15, 678 (2019)

    2019

  53. [61]

    Corboz and F

    P. Corboz and F. Mila, Crystals of bound states in the magnetization plateaus of the shastry-sutherland model, Phys. Rev. Lett. 112, 147203 (2014)

    2014

  54. [62]

    Haegeman, The code is developed with TensorKit package at https://github.com/Jutho/TensorKit.jl

    J. Haegeman, The code is developed with TensorKit package at https://github.com/Jutho/TensorKit.jl. 7 CONTENTS References 5 A. Additional results for the Shastry-Sutherland model 7

  55. [63]

    Comparison of the ground state energies 7

  56. [64]

    The AFM order parameter 7

  57. [65]

    The VBS order parameter 7

  58. [66]

    Generalized model and convergence 8

    The first derivative of the ground state energy 7 B. Generalized model and convergence 8

  59. [67]

    The first derivative of the ground state energy 8

  60. [68]

    The correlation ratio of the AFM order 9 Appendix A: Additional results for the Shastry-Sutherland model

  61. [69]

    S1, we show the energies of the Shastry- Sutherland model on cylinders with different sizes at α := J1/J3 = 0.80

    Comparison of the ground state energies In Fig. S1, we show the energies of the Shastry- Sutherland model on cylinders with different sizes at α := J1/J3 = 0.80. The finite size scaling from the lin- ear extrapolation gives energy ( −0.44844(8)) aligns with a recent extrapolat...

  62. [70]

    The value of m2 at momentum (π, π) is shown in Fig

    The AFM order parameter We calculate the N´ eel AFM order parameter m2 s(k) = 1 L4 X ij ⟨Si · Sj⟩eik·(i−j) (S1) where i = (ix, iy) and k = (π, π) using the middle region of size L × L in an open cylinder of size L × 2L. The value of m2 at momentum (π, π) is shown in Fig. S3. W...

  63. [71]

    S4, which shows that ⟨Dx⟩2 = ⟨Dy⟩2, consistent with a plaquette VBS

    The VBS order parameter We also calculate the VBS order parameter, as shown in Fig. S4, which shows that ⟨Dx⟩2 = ⟨Dy⟩2, consistent with a plaquette VBS. As depicted in Fig. S6 for 14 × 28 system at α = 0.76, plaquettes are formed on the empty squares of the Shastry-Sutherland ...

  64. [72]

    Here, we compare the results obtained from L × 2L (main plot) and L × 2.5L (inset) systems as illustrated in Fig

    The first derivative of the ground state energy As mentioned in the main text, the first derivative of the ground state energy for L × 2L systems also exhibits a crossing point. Here, we compare the results obtained from L × 2L (main plot) and L × 2.5L (inset) systems as illus...

  65. [73]

    The first derivative of the ground state energy In the model interpolating the Shastry-Sutherland lat- tice and J1-J2 model, the first derivative of the ground state energy corresponds to the expectation value of the 9 -0.4039-0.47763 -0.3840-0.1947 -0.4040-0.47771 -0.3842-0.1...

    1947

  66. [74]

    For most results, linear fits with trun- cation error are applied to reduce the finite bond dimen- sion effect

    The correlation ratio of the AFM order The correlation ratio for the AFM order parameter converges rapidly with the bond dimension, only exhibit- ing slower convergence near the transition point at very large system sizes. For most results, linear fits with trun- cation error ...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.