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arXiv:2412.17913 · Physical Review Letters

Quantum Entanglement of XY-Type Spin Dimers on the Shastry-Sutherland Lattice

Anonymous, Brianna R. Billingsley, Alin Niraula, Madalynn Marshall, David Dahlbom, Yiqing Hao, Daniel M. Pajerowski, Alexander I. Kolesnikov, Xiaojian Bai, Cristian D. Batista, Tai Kong, Huibo B. Cao

Published Jul 16, 2026• 1 citation
arXivHTMLPDF

Abstract

We report a comprehensive study on the origin of the enigmatic disordered ground state within the Shastry-Sutherland lattice, BaCe_{2}ZnS_{5}, at low temperatures. The magnetization and heat capacity data show a lack of magnetic ordering down to 73 mK. We deploy a localized spin dimer model which can accurately reproduce the dynamic structure factor of the neutron data, magnetization, and heat capacity data. Remarkably, the intradimer exchange interaction shows strong XY-type anisotropy and the ground state of BaCe_{2}ZnS_{5} is in an entangled state (|↑↑⟩-|↓↓⟩)/sqrt[2]. This is in contrast to the singlet dimer state that is obtained for Heisenberg interactions. These results confirm that BaCe_{2}ZnS_{5} is in a quantum paramagnet state consisting of entangled spin dimer states.

DOI
10.1103/gl65-17z7

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APS Open Science•Apr 29, 2026•0 citations
We report a comprehensive study on the origin of the enigmatic disordered ground state within the Shastry-Sutherland lattice, BaCe_{2}ZnS_{5}, at low temperatures. The magnetization and heat capacity data show a lack of magnetic ordering down to 73 mK. We deploy a localized spin dimer model which can accurately reproduce the dynamic structure factor of the neutron data, magnetization, and heat capacity data. Remarkably, the intradimer exchange interaction shows strong XY-type anisotropy and the ground state of BaCe_{2}ZnS_{5} is in an entangled state (|↑↑⟩-|↓↓⟩)/sqrt[2]. This is in contrast to the singlet dimer state that is obtained for Heisenberg interactions. These results confirm that BaCe_{2}ZnS_{5} is in a quantum paramagnet state consisting of entangled spin dimer states.
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.
Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu _2 2 (BO _3 3 ) _2 2 , which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extended hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization plateaux for moderate values of the interdimer coupling. A possible existence of a striking quantum phase of bound triplons is also revealed at low enough magnetic fields.
The two dimensional Heisenberg model for SrCu2(BO3)2{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ has an exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N\'eel ordered state is determined. Analysis of the experimental data shows that SrCu2(BO3)2\mathrm{SrCu}{}_{2}(\mathrm{BO}{}_{3}{)}_{2}SrCu2​(BO3​)2​ has the dimer ground state but its coupling constants are close to the transition point, which leads to an unusual temperature dependence of the susceptibility. The almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.
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.
Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.
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.