Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2502.14091 · Physical Review Letters

Quantum Spin Liquid Phase in the Shastry-Sutherland Model Revealed by High-Precision Infinite Projected Entangled-Pair States

Philippe Corboz, Yining Zhang, Boris Ponsioen, Frédéric Mila

Published Apr 13, 2026• 6 citations
arXivHTMLPDF

Abstract

The Shastry-Sutherland model is an effective model of the layered material SrCu_{2}(BO_{3})_{2}, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states, a two-dimensional tensor network Ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range 0.785(5)≤J^{'}/J≤0.82(1).

DOI
10.1103/67xm-5d8v

Related papers

Tensor network study of the Shastry-Sutherland model with weak interlayer coupling

Patrick C. G. Vlaar, Philippe Corboz

The layered material SrCu _2 2 (BO _3 3 ) _2 2 has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu _2 2 (BO _3 3 ) _2 2 under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around J''/J\sim0.04-0.05 J ″ / J ∼ 0.04 − 0.05 than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu _2 2 (BO _3 3 ) _2 2 to be around J''/J\sim 0.027 J ″ / J ∼ 0.027 at ambient pressure.

arXiv:2302.07894•SciPost Physics•Oct 2, 2023•6 citations

Tensor network study of the Shastry-Sutherland model in zero magnetic field

Philippe Corboz, Frédéric Mila

We simulate the Shastry-Sutherland model in two dimensions by means of infinite projected entangled-pair states (iPEPS)---a variational tensor network method where the accuracy can be systematically controlled by the so-called bond dimension. Besides the well-established dimer and N\'eel phase iPEPS confirms the presence of an intermediate phase with plaquette long-range order, and we determine its phase boundaries with high accuracy. The first-order phase transition for $J=0.675(2)$ between dimer and plaquette phase is compatible with previous series expansion results. iPEPS predicts a weak first-order phase transition between plaquette and N\'eel phase occurring for $J=0.765(15)$. We do not find a stable intermediate columnar-dimer phase, even when we bias the state towards this order.

arXiv:1212.2983•Physical Review B•Mar 27, 2013•190 citations

On the precise boundary of the Néel antiferromagnetic phase in the Shastry-Sutherland model

Rongyi Lv, Xiangjian Qian, Mingpu Qin

The ground state phase diagram of the Shastry-Sutherland model remains controversial. In particular, the nature of the transition between the plaquette valence bond solid (PVBS) phase and the Néel antiferromagnetic (AFM) phase is still under debate. While some studies suggest a direct transition between the two phases, others propose the existence of a narrow intermediate quantum spin liquid regime. To address this issue, we perform large-scale Density Matrix Renormalization Group calculations to determine the Néel AFM phase boundary in the Shastry-Sutherland model. By applying staggered boundary pinning fields and directly measuring the bulk staggered magnetization, and through systematic extrapolations with respect to truncation error as well as careful finite-size scaling, we find that the staggered magnetization remains finite across the controversial region $0.78 \lesssim J_{1}/J_{2} \leq 0.81$, which was suggested to host a quantum spin liquid phase in some studies. Together with the previously established consensus placing the PVBS phase boundary at $J_{1}/J_{2} \approx 0.78$, these results provide evidence against the existence of an intermediate quantum spin liquid phase and support a direct PVBS--Néel AFM transition in the Shastry-Sutherland model.

arXiv:2609.22907•Sep 19, 2026•0 citations

Quantum Criticality with Emergent Symmetry in the Extended Shastry-Sutherland Model

Wen-Yuan Liu, Xiaotian Zhang, Zhe Wang +3 more

Motivated by the novel phenomena observed in the layered material SrCu_{2}(BO_{3})_{2}, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu_{2}(BO_{3})_{2}. However, the nature of its quantum phase transition from the plaquette valence-bond solid to antiferromagnetic phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to 20×20 sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the plaquette valence-bond solid and antiferromagnetic phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of SrCu_{2}(BO_{3})_{2}.

arXiv:2309.10955•Physical Review Letters•Jul 9, 2024•17 citations

Quantum criticality and spin liquid phase in the Shastry-Sutherland model

Jianwei Yang, Anders W. Sandvik, Ling Wang

The two-dimensional quantum spin model proposed by Shastry and Sutherland more than four decades ago is notable for its realization in SrCu${}_{2}$(BO${}_{3}$)${}_{2}$. Here, the authors present numerical evidence of a gapless spin liquid phase in the model and discuss its connection to a deconfined quantum critical point. The new phase exists in a parameter regime where recent high-pressure heat capacity measurements on SrCu${}_{2}$(BO${}_{3}$)${}_{2}$ did not detect any low-temperature order, in contrast to the antiferromagnetic and plaquette-singlet phases existing at higher and lower pressures, respectively. Thus, the elusive spin liquid may exist in SrCu${}_{2}$(BO${}_{3}$)${}_{2}$.

arXiv:2104.08887•Physical review. B./Physical review. B•Feb 23, 2022•88 citations

Tensor network study of the m=12 magnetization plateau in the Shastry-Sutherland model at finite temperature

Piotr Czarnik, Marek M. Rams, Philippe Corboz +1 more

The two-dimensional infinite projected entangled pair state tensor network is evolved in imaginary time with the full update (FU) algorithm to simulate the Shastry-Sutherland model in a magnetic field at finite temperature directly in the thermodynamic limit. We focus on the phase transition into the $m=\frac{1}{2}$ magnetization plateau, which was observed in experiments on ${\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}$. For the largest simulated bond dimension, the early evolution in the high-temperature regime is simulated with the simple update (SU) scheme and then, as the correlation length increases, continued with the FU scheme towards the critical regime. We apply a small symmetry-breaking bias field and then extrapolate towards zero bias using a simple scaling theory in the bias field. The combined SU $+$ FU scheme provides an accurate estimate of the critical temperature, even though the results could not be fully converged in the bond dimension in the vicinity of the transition. The critical temperature estimate is improved with a generalized scaling theory that combines two divergent length scales: One due to the bias, and the other due to the finite bond dimension. The obtained results are consistent with the transition being in the universality class of the two-dimensional classical Ising model. The estimated critical temperature is 3.5(2) K, which is well above the temperature 2.1 K used in the experiments.

arXiv:2012.05265•Physical review. B./Physical review. B•Feb 4, 2021•41 citations
The Shastry-Sutherland model is an effective model of the layered material SrCu_{2}(BO_{3})_{2}, which exhibits an extremely rich phase diagram as a function of pressure and magnetic field. Motivated by the recent controversy regarding its phase diagram at zero magnetic field, we perform large-scale simulations based on infinite projected entangled-pair states, a two-dimensional tensor network Ansatz to represent the ground state directly in the thermodynamic limit. By employing the latest optimization techniques, we obtain variational states with lower energy than previous results obtained from other methods. Using systematic extrapolations to the exact infinite bond dimension limit, our simulations reveal a narrow quantum spin liquid phase between the plaquette and antiferromagnetic phases in the range 0.785(5)≤J^{'}/J≤0.82(1).
The layered material SrCu _2 2 (BO _3 3 ) _2 2 has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu _2 2 (BO _3 3 ) _2 2 under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around J''/J\sim0.04-0.05 J ″ / J ∼ 0.04 − 0.05 than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu _2 2 (BO _3 3 ) _2 2 to be around J''/J\sim 0.027 J ″ / J ∼ 0.027 at ambient pressure.
We simulate the Shastry-Sutherland model in two dimensions by means of infinite projected entangled-pair states (iPEPS)---a variational tensor network method where the accuracy can be systematically controlled by the so-called bond dimension. Besides the well-established dimer and N\'eel phase iPEPS confirms the presence of an intermediate phase with plaquette long-range order, and we determine its phase boundaries with high accuracy. The first-order phase transition for J=0.675(2)J=0.675(2)J=0.675(2) between dimer and plaquette phase is compatible with previous series expansion results. iPEPS predicts a weak first-order phase transition between plaquette and N\'eel phase occurring for J=0.765(15)J=0.765(15)J=0.765(15). We do not find a stable intermediate columnar-dimer phase, even when we bias the state towards this order.
The ground state phase diagram of the Shastry-Sutherland model remains controversial. In particular, the nature of the transition between the plaquette valence bond solid (PVBS) phase and the Néel antiferromagnetic (AFM) phase is still under debate. While some studies suggest a direct transition between the two phases, others propose the existence of a narrow intermediate quantum spin liquid regime. To address this issue, we perform large-scale Density Matrix Renormalization Group calculations to determine the Néel AFM phase boundary in the Shastry-Sutherland model. By applying staggered boundary pinning fields and directly measuring the bulk staggered magnetization, and through systematic extrapolations with respect to truncation error as well as careful finite-size scaling, we find that the staggered magnetization remains finite across the controversial region 0.78≲J1/J2≤0.810.78 \lesssim J_{1}/J_{2} \leq 0.810.78≲J1​/J2​≤0.81, which was suggested to host a quantum spin liquid phase in some studies. Together with the previously established consensus placing the PVBS phase boundary at J1/J2≈0.78J_{1}/J_{2} \approx 0.78J1​/J2​≈0.78, these results provide evidence against the existence of an intermediate quantum spin liquid phase and support a direct PVBS--Néel AFM transition in the Shastry-Sutherland model.
Motivated by the novel phenomena observed in the layered material SrCu_{2}(BO_{3})_{2}, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu_{2}(BO_{3})_{2}. However, the nature of its quantum phase transition from the plaquette valence-bond solid to antiferromagnetic phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to 20×20 sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the plaquette valence-bond solid and antiferromagnetic phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of SrCu_{2}(BO_{3})_{2}.
The two-dimensional quantum spin model proposed by Shastry and Sutherland more than four decades ago is notable for its realization in SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​. Here, the authors present numerical evidence of a gapless spin liquid phase in the model and discuss its connection to a deconfined quantum critical point. The new phase exists in a parameter regime where recent high-pressure heat capacity measurements on SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ did not detect any low-temperature order, in contrast to the antiferromagnetic and plaquette-singlet phases existing at higher and lower pressures, respectively. Thus, the elusive spin liquid may exist in SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​.
The two-dimensional infinite projected entangled pair state tensor network is evolved in imaginary time with the full update (FU) algorithm to simulate the Shastry-Sutherland model in a magnetic field at finite temperature directly in the thermodynamic limit. We focus on the phase transition into the m=12m=\frac{1}{2}m=21​ magnetization plateau, which was observed in experiments on SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​. For the largest simulated bond dimension, the early evolution in the high-temperature regime is simulated with the simple update (SU) scheme and then, as the correlation length increases, continued with the FU scheme towards the critical regime. We apply a small symmetry-breaking bias field and then extrapolate towards zero bias using a simple scaling theory in the bias field. The combined SU +++ FU scheme provides an accurate estimate of the critical temperature, even though the results could not be fully converged in the bond dimension in the vicinity of the transition. The critical temperature estimate is improved with a generalized scaling theory that combines two divergent length scales: One due to the bias, and the other due to the finite bond dimension. The obtained results are consistent with the transition being in the universality class of the two-dimensional classical Ising model. The estimated critical temperature is 3.5(2) K, which is well above the temperature 2.1 K used in the experiments.