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:2507.13877

Exact ground state on the 3D analogue of the Shastry-Sutherland model

Kelvin Salou-Smith, Arnaud Ralko, Ludovic D. C. Jaubert

Published Jul 18, 2025• 0 citations
arXivHTMLPDF

Abstract

Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet ground state. In this work, we introduce a three-dimensional analogue of the SS lattice, constructed by deforming the pyrochlore lattice to preserve the local SS geometry. Despite the dimensional increase and altered topology, the ground-state phase diagrams of classical Ising and Heisenberg spins, remain analytically tractable and closely follow their 2D counterparts, including the existence of a 1/3 magnetization plateau and umbrella states. Most notably, for quantum spins S = 1/2, the dimer singlet state survives as an exact ground state over a finite region of the phase diagram. We argue, using exact diagonalization, that the singlet phase is stabilized beyond its 2D counterpart, suggesting enhanced robustness in three dimensions. These results offer a rare, controlled platform to explore the impact of dimensionality on quantum frustration, exact solvability, and potential spin liquid behavior in 3D, with relevance to emergent topological and magnetic phases.

DOI
10.48550/arxiv.2507.13877

Related papers

Theory of rare-earth Kramers magnets on a shastry-sutherland lattice: dimer phases in the presence of strong spin-orbit coupling

Changle Liu, Guijing Duan, Rong Yu

Shastry-Sutherland magnet is a typical frustrated spin system hosting rich phases. While the Heisenberg limit has been extensively studied, the role of spin-orbit coupling is not well explored. Motivated by newly discovered rare-earth Shastry-Sutherland magnets, we construct a generic effective-spin model that describes the interactions between Kramers doublet local moments on a Shastry-Sutherland lattice. Due to the strong spin-orbit coupling, the model takes the form of extended XYZ interactions on both intra- and inter-dimer bonds. We show that, in addition to the conventional “singlet” dimer phase, strong spin-orbit coupling can stabilize peculiar “triplet” dimer phases. These “triplet” dimer phases, though fully gapped, respond immediately to magnetic fields and evolve smoothly into the fully polarized phase. We present that the recently discovered Shastry-Sutherland magnet Yb 2 Be 2 GeO 7 belongs to the “triplet” dimer phase, and discuss the implication of our results to a broad class of quantum magnets in general.

arXiv:2412.00757•npj Quantum Materials•Dec 3, 2025•5 citations

Quantum phase diagram of ferromagnetically coupled singlet dimers on a distorted Shastry-Sutherland lattice

Monalisa Chatterjee, Santanu Pal, Manjit Kumar

Frustrated spin-1/2 model with all-antiferromagnetic exchange on Shastry-Sutherland lattice (SSL) has been extensively explored, and in this work we study the quantum phase diagram of isotropic Heisenberg spin- 1 / 2 model on the SSL with ferromagnetic exchange interactions along leg, and antiferromagnetic couplings along the diagonal bonds ( J ). Using density matrix renormalization group (DMRG) and exact diagonalization calculations, we identify four distinct ground-state (gs) phases for this frustrated spin-1/2 model: stripe ( π , 0 ) , stripe ( 0 , π ) , ferromagnetic, and spiral-dimer phases. In the spiral-dimer phase the gs can exhibit dimer formation along the diagonal bonds with or without spins spiral along the x axis or y axis in different parameter regime and these states are connected through crossovers. There is a continuous transition between stripe with a long-range spin-spin correlations and spiral-dimer phase with a short-range correlations. An effective spin parameter is introduced to accurately determine the phase boundaries. Our DMRG results differ significantly from previous Schwinger boson mean-field theory predictions. The spiral phase occurs in a narrow range of the parameter space and shows short-range correlations in the system.

APS Open Science•Apr 29, 2026•0 citations

Chiral spin liquid on a Shastry-Sutherland Heisenberg antiferromagnet

Jian-Wei Yang, Weiwei Luo, W. Zhu +3 more

We demonstrate the existence of a topological chiral spin liquid in the frustrated Shastry-Sutherland Heisenberg model with an additional spin chirality interaction, using numerically unbiased exact diagonalization and density matrix renormalization group methods. We establish a quantum phase diagram where conventional phases, including dimer singlet, plaquette singlet, N\'eel, and collinear phase, can be clearly identified by suitable local order parameters. Among them, an $\text{SU}{(2)}_{1}$ chiral spin liquid emerges in the highly frustrated region, which is unambiguously identified by two topologically degenerate ground states, a modular matrix, and characteristic level counting in an entanglement spectrum, featuring the same topological order of the $\ensuremath{\nu}=1/2$ bosonic Laughlin state. The phase boundaries among the different orders are determined by the energy level crossing analysis and wave-function fidelity susceptibility.

arXiv:2403.00597•Physical review. B./Physical review. B•May 3, 2024•1 citation

Analog quantum simulation of Shastry-Sutherland Ising materials

Vahagn Mkhitaryan, Milan Kornjača, Mao Lin +17 more

Frustrated magnets host rich emergent behavior because competing interactions generate dense manifolds of low-energy states. The Ising Shastry-Sutherland model is a paradigmatic setting, motivated experimentally by Ising-like rare-earth tetraborides such as TmB$_4$ and ErB$_4$, whose field-induced magnetization plateaus have motivated extensive microscopic modeling. Yet how tunable quantum fluctuations reorganize this material-motivated phase diagram remains largely unexplored. Here, we realize a transverse- and longitudinal-field Ising model on the Shastry-Sutherland lattice using a programmable Rydberg-atom array. We map its quantum phase diagram using density matrix renormalization group calculations and probe corresponding signatures experimentally in arrays containing more than 110 atoms. Beyond the established classical phases, the calculations identify two regimes absent in the classical limit and stabilized at finite transverse field: a $2/5$ filling plateau whose finite stability region emerges from a classically degenerate phase boundary and a symmetry-preserving quantum-dimer regime replacing classically selected collinear order. Experiments on finite open arrays reveal signatures consistent with these regimes across three boundary-pinning conditions, with the resulting response maps agreeing qualitatively with the calculated phase diagram. Our results establish programmable Rydberg-atom arrays as tools for exploring frustrated, material-motivated Hamiltonians and motivate searches for new, quantum-driven magnetization plateaus and quantum-dimer behavior in ErB$_4$ under a transverse field or in strain-tuned TmB$_4$.

quant-pharXiv:2610.12800•Oct 12, 2026•0 citations

Identifying the ground state phases by spin-patterns in the Shastry-Sutherland model

Yun-Tong Yang, Fuzhou Chen, Hong‐Gang Luo

Exploring the influence of frustration on the phases and related phase transitions in condensed matter physics is of fundamental importance in uncovering the role played by frustration. In the two-dimensional square lattice, a minimal frustration has been formulated in 1981 as the Shastry-Sutherland (SS) model described by competitions between the nearest-neighbor bond ($J_1$) and the next-nearest-neighbor one ($J_2$). In the two limits of $α=J_2/J_1$, i.e. $α\ll 1$ and $α\gg 1$, the corresponding phases are the N{é}el antiferromagnet (AFM) and the dimer-singlet(DS). Unfortunately, the intermediate regime remains controversial, and the nature of transition from the N{é}el AFM to the intermediate state is also unclear. Here we provide a pattern language to explore the SS model and take the lattice size $L=4 \times4$ with periodic boundary condition. We firstly diagonalize the Hamiltonian in an operator space to obtain all fundamental spin-patterns and then analyze their energy and occupancy evolutions with the frustration parameter $κ=α/ (1+α)$. Our results indicate that the intermediate regime is characterized by diagonal two-domain spin-pattern while the N{é}el AFM state has a diagonal single-domain and the DS has mixings of diagonal single- and four-domain. While the transition from the DS to the intermediate phase occurred around $α_c = 1.5$ is the first-order in nature, consistent with that in literature, the one from the intermediate phase to the AFM is clearly seen around $α_c = 1.277$, where it has a reversal of the contributions from the single- and two-domain patterns to the ground state. The result indicates that the pattern language is powerful in identifying the possible phases in frustrated models.

arXiv:2404.16330•Apr 25, 2024•0 citations

Exact ground states of a spin- 12 Ising-Heisenberg model on the Shastry-Sutherland lattice in a magnetic field

Taras Verkholyak, Jozef Strečka, Frédéric Mila +1 more

Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intradimer and Ising interdimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of ${\mathrm{SrCu}}_{2}{(\mathrm{BO}}_{3}){}_{2}$ and ${(\mathrm{CuCl})\mathrm{Ca}}_{2}{\mathrm{Nb}}_{3}{\mathrm{O}}_{10}$ can be described within the suggested Ising-Heisenberg model.

arXiv:1407.8229•Physical Review B•Oct 16, 2014•26 citations
Exact results in frustrated quantum many-body systems are rare, especially in dimensions higher than one. The Shastry-Sutherland (SS) model stands out as a rare example of a two-dimensional spin system with an exactly solvable dimer singlet ground state. In this work, we introduce a three-dimensional analogue of the SS lattice, constructed by deforming the pyrochlore lattice to preserve the local SS geometry. Despite the dimensional increase and altered topology, the ground-state phase diagrams of classical Ising and Heisenberg spins, remain analytically tractable and closely follow their 2D counterparts, including the existence of a 1/3 magnetization plateau and umbrella states. Most notably, for quantum spins S = 1/2, the dimer singlet state survives as an exact ground state over a finite region of the phase diagram. We argue, using exact diagonalization, that the singlet phase is stabilized beyond its 2D counterpart, suggesting enhanced robustness in three dimensions. These results offer a rare, controlled platform to explore the impact of dimensionality on quantum frustration, exact solvability, and potential spin liquid behavior in 3D, with relevance to emergent topological and magnetic phases.
Shastry-Sutherland magnet is a typical frustrated spin system hosting rich phases. While the Heisenberg limit has been extensively studied, the role of spin-orbit coupling is not well explored. Motivated by newly discovered rare-earth Shastry-Sutherland magnets, we construct a generic effective-spin model that describes the interactions between Kramers doublet local moments on a Shastry-Sutherland lattice. Due to the strong spin-orbit coupling, the model takes the form of extended XYZ interactions on both intra- and inter-dimer bonds. We show that, in addition to the conventional “singlet” dimer phase, strong spin-orbit coupling can stabilize peculiar “triplet” dimer phases. These “triplet” dimer phases, though fully gapped, respond immediately to magnetic fields and evolve smoothly into the fully polarized phase. We present that the recently discovered Shastry-Sutherland magnet Yb 2 Be 2 GeO 7 belongs to the “triplet” dimer phase, and discuss the implication of our results to a broad class of quantum magnets in general.
Frustrated spin-1/2 model with all-antiferromagnetic exchange on Shastry-Sutherland lattice (SSL) has been extensively explored, and in this work we study the quantum phase diagram of isotropic Heisenberg spin- 1 / 2 model on the SSL with ferromagnetic exchange interactions along leg, and antiferromagnetic couplings along the diagonal bonds ( J ). Using density matrix renormalization group (DMRG) and exact diagonalization calculations, we identify four distinct ground-state (gs) phases for this frustrated spin-1/2 model: stripe ( π , 0 ) , stripe ( 0 , π ) , ferromagnetic, and spiral-dimer phases. In the spiral-dimer phase the gs can exhibit dimer formation along the diagonal bonds with or without spins spiral along the x axis or y axis in different parameter regime and these states are connected through crossovers. There is a continuous transition between stripe with a long-range spin-spin correlations and spiral-dimer phase with a short-range correlations. An effective spin parameter is introduced to accurately determine the phase boundaries. Our DMRG results differ significantly from previous Schwinger boson mean-field theory predictions. The spiral phase occurs in a narrow range of the parameter space and shows short-range correlations in the system.
We demonstrate the existence of a topological chiral spin liquid in the frustrated Shastry-Sutherland Heisenberg model with an additional spin chirality interaction, using numerically unbiased exact diagonalization and density matrix renormalization group methods. We establish a quantum phase diagram where conventional phases, including dimer singlet, plaquette singlet, N\'eel, and collinear phase, can be clearly identified by suitable local order parameters. Among them, an SU(2)1\text{SU}{(2)}_{1}SU(2)1​ chiral spin liquid emerges in the highly frustrated region, which is unambiguously identified by two topologically degenerate ground states, a modular matrix, and characteristic level counting in an entanglement spectrum, featuring the same topological order of the $\ensuremath{\nu}=1/2$ bosonic Laughlin state. The phase boundaries among the different orders are determined by the energy level crossing analysis and wave-function fidelity susceptibility.
Frustrated magnets host rich emergent behavior because competing interactions generate dense manifolds of low-energy states. The Ising Shastry-Sutherland model is a paradigmatic setting, motivated experimentally by Ising-like rare-earth tetraborides such as TmB4_44​ and ErB4_44​, whose field-induced magnetization plateaus have motivated extensive microscopic modeling. Yet how tunable quantum fluctuations reorganize this material-motivated phase diagram remains largely unexplored. Here, we realize a transverse- and longitudinal-field Ising model on the Shastry-Sutherland lattice using a programmable Rydberg-atom array. We map its quantum phase diagram using density matrix renormalization group calculations and probe corresponding signatures experimentally in arrays containing more than 110 atoms. Beyond the established classical phases, the calculations identify two regimes absent in the classical limit and stabilized at finite transverse field: a 2/52/52/5 filling plateau whose finite stability region emerges from a classically degenerate phase boundary and a symmetry-preserving quantum-dimer regime replacing classically selected collinear order. Experiments on finite open arrays reveal signatures consistent with these regimes across three boundary-pinning conditions, with the resulting response maps agreeing qualitatively with the calculated phase diagram. Our results establish programmable Rydberg-atom arrays as tools for exploring frustrated, material-motivated Hamiltonians and motivate searches for new, quantum-driven magnetization plateaus and quantum-dimer behavior in ErB4_44​ under a transverse field or in strain-tuned TmB4_44​.
Exploring the influence of frustration on the phases and related phase transitions in condensed matter physics is of fundamental importance in uncovering the role played by frustration. In the two-dimensional square lattice, a minimal frustration has been formulated in 1981 as the Shastry-Sutherland (SS) model described by competitions between the nearest-neighbor bond (J1J_1J1​) and the next-nearest-neighbor one (J2J_2J2​). In the two limits of α=J2/J1α=J_2/J_1α=J2​/J1​, i.e. α≪1α\ll 1α≪1 and α≫1α\gg 1α≫1, the corresponding phases are the N{é}el antiferromagnet (AFM) and the dimer-singlet(DS). Unfortunately, the intermediate regime remains controversial, and the nature of transition from the N{é}el AFM to the intermediate state is also unclear. Here we provide a pattern language to explore the SS model and take the lattice size L=4×4L=4 \times4L=4×4 with periodic boundary condition. We firstly diagonalize the Hamiltonian in an operator space to obtain all fundamental spin-patterns and then analyze their energy and occupancy evolutions with the frustration parameter κ=α/(1+α)κ=α/ (1+α)κ=α/(1+α). Our results indicate that the intermediate regime is characterized by diagonal two-domain spin-pattern while the N{é}el AFM state has a diagonal single-domain and the DS has mixings of diagonal single- and four-domain. While the transition from the DS to the intermediate phase occurred around αc=1.5α_c = 1.5αc​=1.5 is the first-order in nature, consistent with that in literature, the one from the intermediate phase to the AFM is clearly seen around αc=1.277α_c = 1.277αc​=1.277, where it has a reversal of the contributions from the single- and two-domain patterns to the ground state. The result indicates that the pattern language is powerful in identifying the possible phases in frustrated models.
Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intradimer and Ising interdimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2{\mathrm{SrCu}}_{2}{(\mathrm{BO}}_{3}){}_{2}SrCu2​(BO3​)2​ and (CuCl)Ca2Nb3O10{(\mathrm{CuCl})\mathrm{Ca}}_{2}{\mathrm{Nb}}_{3}{\mathrm{O}}_{10}(CuCl)Ca2​Nb3​O10​ can be described within the suggested Ising-Heisenberg model.