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:2406.10689 · Physical review. B./Physical review. B

Weakly first-order melting of the 1/3 plateau in the Shastry-Sutherland model

Samuel Nyckees, Philippe Corboz, Frédéric Mila

Published Jan 21, 2025• 3 citations
arXivHTMLPDF

Abstract

We investigate the thermal properties of the $\frac{1}{3}$ plateau in the Shastry-Sutherland model with infinite projected entangled-pair states by performing the imaginary-time evolution of the infinite-temperature density matrix. We show that both the ${\mathbb{Z}}_{2}$ and ${\mathbb{Z}}_{3}$ broken symmetries of the ground state are restored at a unique temperature where the correlation length has a peak, and that the melting of the plateau occurs via a single weakly first-order transition. We focus on the experimentally relevant coupling constants deep into the $\frac{1}{3}$ plateau phase at $h=1$ and ${J}^{\ensuremath{'}}/J=0.63$, which was estimated to describe the ${\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}$ compound. By computing the free energy we are able to locate the transition temperature around ${T}_{c}\ensuremath{\simeq}4.8\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, well above the temperature $T=2\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ at which the $\frac{1}{3}$ plateau was observed in experiments. The investigation is supplemented by adding a bias term to the Hamiltonian and studying the induced crossover. We further map the transition line in the field-temperature phase diagram.

DOI
10.1103/physrevb.111.014428

Related papers

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

Thermally populated versus field-induced triplon bound states in the Shastry-Sutherland lattice SrCu2(BO3)2

Dirk Wulferding, Y. S. Choi, Seung‐Yeol Lee +6 more

Abstract The Shastry–Sutherland compound SrCu2(BO3)2constituting orthogonally coupled dimers harbors anS = 0 singlet ground state. The confluence of strong interdimer interaction and frustration engenders a spectrum of low-energy excitations including localized triplons as well as singlet and triplet bound states. Their dynamics are controlled by an external magnetic field and temperature. Here, we employ high-field Raman spectroscopy to map the field and temperature evolution of such bosonic composite quasiparticles on approaching the 1/8 magnetization plateau. Our study unveils that the magnetic field and thermal fluctuations show remarkably similar effects in melting the singlet bound states, but are disparate in their effects on the fine spectral shapes. This, together with the anti-crossing of two singlet bound states in the intermediate fieldB = 10 − 16 T, is discussed in terms of the correlated dynamics of frustrated, interacting bosons.

arXiv:2111.13354•npj Quantum Materials•Dec 17, 2021•9 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

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

Philippe Corboz, Yining Zhang, Boris Ponsioen +1 more

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).

arXiv:2502.14091•Physical Review Letters•Apr 13, 2026•6 citations

Theoretical and experimental studies of melting of the 1/3 magnetization plateau in a frustrated $$S=1/2$$ antiferromagnetic trimerized quantum Heisenberg spin chain compound $$\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}$$

Sachin Kumar, Anup Kumar Bera, Amit Kumar +2 more

Abstract We report the magnetization process of $$S=1/2$$ S = 1 / 2 Heisenberg antiferromagnetic $$J_1{-}J_1{-}J_2$$ J 1 - J 1 - J 2 trimerized spin chain system (with frustration due to the next-nearest-neighbor interaction $$J_3$$ J 3 within the trimer) under applied magnetic field by means of density-matrix renormalization group method. Here, $$J'$$ J ′ s are the antiferromagnetic exchange interaction constants. Specifically, we explore the phenomenon of 1/3 magnetization plateau for the exchange coupling ratios $$ \alpha = 0.18, \beta =0.18 $$ α = 0.18 , β = 0.18 , and $$J_1=235$$ J 1 = 235 K, where $$\alpha =J_2/J_1$$ α = J 2 / J 1 , and $$\beta =J_3/J_1$$ β = J 3 / J 1 as found for the model compound $$\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}$$ Na 2 Cu 3 Ge 4 O 12 . It is found that a wide 1/3 quantum magnetization plateau state (observed in ground state magnetization) gradually disappears with increasing temperature beyond a crossover temperature $$T_{co}$$ T co due to thermal fluctuations. Based on numerical data, the width w(T) of the magnetization plateau is found to follow an exponential behave as $$\sim e^{-B/\sqrt{T_{co}-T}}$$ ∼ e - B / T co - T , where B is a constant and $$T_{co}$$ T co is estimated to be $$ \approx 60$$ ≈ 60

The European Physical Journal B•Mar 1, 2025•1 citation

Magnetic properties of the spin- 12 XXZ model on the Shastry-Sutherland lattice: Effect of long-range interactions

Takahumi Suzuki, Yusuke Tomita, Naoki Kawashima

We study magnetic properties of the spin-$\frac{1}{2}$ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We investigate the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the two-dimensional Ising model universality although there is a single phase transition in the Ising limit case. Finally, we estimate the coupling ratio to explain the magnetization process observed in ${\text{TmB}}_{4}$.

arXiv:0910.4162•Physical Review B•Nov 5, 2009•35 citations
We investigate the thermal properties of the 13\frac{1}{3}31​ plateau in the Shastry-Sutherland model with infinite projected entangled-pair states by performing the imaginary-time evolution of the infinite-temperature density matrix. We show that both the Z2{\mathbb{Z}}_{2}Z2​ and Z3{\mathbb{Z}}_{3}Z3​ broken symmetries of the ground state are restored at a unique temperature where the correlation length has a peak, and that the melting of the plateau occurs via a single weakly first-order transition. We focus on the experimentally relevant coupling constants deep into the 13\frac{1}{3}31​ plateau phase at h=1h=1h=1 and J\ensuremath′/J=0.63{J}^{\ensuremath{'}}/J=0.63J\ensuremath′/J=0.63, which was estimated to describe the SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​ compound. By computing the free energy we are able to locate the transition temperature around Tc\ensuremath≃4.8K{T}_{c}\ensuremath{\simeq}4.8\phantom{\rule{0.28em}{0ex}}\mathrm{K}Tc​\ensuremath≃4.8K, well above the temperature T=2KT=2\phantom{\rule{0.28em}{0ex}}\mathrm{K}T=2K at which the 13\frac{1}{3}31​ plateau was observed in experiments. The investigation is supplemented by adding a bias term to the Hamiltonian and studying the induced crossover. We further map the transition line in the field-temperature phase diagram.
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.
Abstract The Shastry–Sutherland compound SrCu2(BO3)2constituting orthogonally coupled dimers harbors anS = 0 singlet ground state. The confluence of strong interdimer interaction and frustration engenders a spectrum of low-energy excitations including localized triplons as well as singlet and triplet bound states. Their dynamics are controlled by an external magnetic field and temperature. Here, we employ high-field Raman spectroscopy to map the field and temperature evolution of such bosonic composite quasiparticles on approaching the 1/8 magnetization plateau. Our study unveils that the magnetic field and thermal fluctuations show remarkably similar effects in melting the singlet bound states, but are disparate in their effects on the fine spectral shapes. This, together with the anti-crossing of two singlet bound states in the intermediate fieldB = 10 − 16 T, is discussed in terms of the correlated dynamics of frustrated, interacting bosons.
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 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).
Theoretical and experimental studies of melting of the 1/3 magnetization plateau in a frustrated S=1/2S=1/2S=1/2 antiferromagnetic trimerized quantum Heisenberg spin chain compound Na2Cu3Ge4O12\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}Na2​Cu3​Ge4​O12​
Abstract We report the magnetization process of S=1/2S=1/2S=1/2 S = 1 / 2 Heisenberg antiferromagnetic J1−J1−J2J_1{-}J_1{-}J_2J1​−J1​−J2​ J 1 - J 1 - J 2 trimerized spin chain system (with frustration due to the next-nearest-neighbor interaction J3J_3J3​ J 3 within the trimer) under applied magnetic field by means of density-matrix renormalization group method. Here, J′J'J′ J ′ s are the antiferromagnetic exchange interaction constants. Specifically, we explore the phenomenon of 1/3 magnetization plateau for the exchange coupling ratios α=0.18,β=0.18 \alpha = 0.18, \beta =0.18 α=0.18,β=0.18 α = 0.18 , β = 0.18 , and J1=235J_1=235J1​=235 J 1 = 235 K, where α=J2/J1\alpha =J_2/J_1α=J2​/J1​ α = J 2 / J 1 , and β=J3/J1\beta =J_3/J_1β=J3​/J1​ β = J 3 / J 1 as found for the model compound Na2Cu3Ge4O12\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}Na2​Cu3​Ge4​O12​ Na 2 Cu 3 Ge 4 O 12 . It is found that a wide 1/3 quantum magnetization plateau state (observed in ground state magnetization) gradually disappears with increasing temperature beyond a crossover temperature TcoT_{co}Tco​ T co due to thermal fluctuations. Based on numerical data, the width w(T) of the magnetization plateau is found to follow an exponential behave as ∼e−B/Tco−T\sim e^{-B/\sqrt{T_{co}-T}}∼e−B/Tco​−T​ ∼ e - B / T co - T , where B is a constant and TcoT_{co}Tco​ T co is estimated to be ≈60 \approx 60≈60 ≈ 60
We study magnetic properties of the spin-12\frac{1}{2}21​ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We investigate the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the two-dimensional Ising model universality although there is a single phase transition in the Ising limit case. Finally, we estimate the coupling ratio to explain the magnetization process observed in TmB4{\text{TmB}}_{4}TmB4​.