The Shastry-Sutherland (SS) model as a canonical example of frustrated magnetism has been extensively studied. The conventional wisdom has been that the transition from the plaquette valence bond order to the Neel order is direct and potentially realizes a deconfined quantum critical point beyond the Ginzburg-Landau paradigm. This scenario, however, was challenged recently by improved numerics from density matrix renormalization group which offers evidence for a narrow gapless spin liquid between the two phases. Prompted by this controversy and to shed light on this intricate parameter regime from a fresh perspective, we report high-resolution functional renormalization group analysis of the generalized SS model. The flows of over 50 million running couplings provide a detailed picture for the evolution of spin correlations as the frequency/energy scale is dialed from the ultraviolet to the infrared to yield the zero-temperature phase diagram. The singlet dimer phase emerges as a fixed point, the Neel order is characterized by divergence in the vertex function, while the transition into and out of the plaquette order is accompanied by pronounced peaks in the plaquette susceptibility. The plaquette order is suppressed before the onset of the Neel order, lending evidence for a finite spin liquid region for ${J}_{1}/{J}_{2}\ensuremath{\in}(0.77,0.82)$, where the flow is continuous without any indication of divergence.
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≤0.81, 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≈0.78, 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.
We study the half-filled single-band Hubbard model on the Shastry–Sutherland lattice with nearest-neighbor hopping
t, incorporating (i) a frustrating diagonal hopping
t′ to probe the emergence of spin-liquid behavior, and (ii) an additional Heisenberg exchange
J that explicitly stabilizes plaquette-singlet correlations. Using the variational cluster approximation (VCA) with exact diagonalization at zero temperature on an eight-site cluster, we map the phase diagrams in the
(U/t,t′/t) and
(U/t,J/t) parameter planes. In the
(U/t,t′/t) plane, our analysis uncovers a competition between N\'eel antiferromagnetic (AFM) order with staggered magnetization and a nonmagnetic regime lacking conventional order, consistent with an algebraic spin-liquid (ASL) phase characterized by a gapped excitation spectrum and vanishing staggered magnetization. In contrast, the
(U/t,J/t) phase diagram exhibits a competition between the N\'eel AFM and a solid valence-bonding valence bond plaquette (PS), where spins form localized singlet plaquettes. Most notably, we observe that the transition from the PS phase to the N\'eel AFM is a first-order phase transition, with a discontinuous jump of the order parameters at the phase boundary, in quantitative agreement with high-pressure heat-capacity measurements on SrCu
2(BO
3)
2 [Guo \emph{et al.}, Commun. Phys. 8, 75 (2025)]. Thus, our VCA analysis underscores the subtle interplay of geometric frustration, quantum fluctuations, and dimensionality, and elucidates the crucial role of short-range correlations in stabilizing and competing ground states of frustrated quantum magnets.
We study the half-filled single-band Hubbard model on the Shastry-Sutherland lattice with nearest-neighbor hopping t , incorporating (i) a frustrating diagonal hopping t ′ to probe the emergence of spin-liquid behavior, and (ii) an additional Heisenberg exchange J that explicitly stabilizes plaquette-singlet correlations. Using the variational cluster approximation (VCA) with exact diagonalization at zero temperature on an eight-site cluster, we map the phase diagrams in the ( U / t , t ′ / t ) and ( U / t , J / t ) parameter planes. In the ( U / t , t ′ / t ) plane, our analysis uncovers a competition between Néel antiferromagnetic (AFM) order with staggered magnetization and a nonmagnetic regime lacking conventional order, consistent with a nonmagnetic insulating phase that may be related to the spin-liquid-like regimes reported in previous studies. In contrast, the ( U / t , J / t ) phase diagram exhibits a competition between the Néel antiferromagnet and a solid valence-bonding valence bond plaquette (PS), where spins form localized singlet plaquettes. Most notably, we observe that the transition from the PS phase to the Néel AFM phase is a first-order phase transition, with a discontinuous jump of the order parameters at the phase boundary, in quantitative agreement with high-pressure heat-capacity measurements on SrCu 2 ( BO 3 ) 2 [J. Guo , ]. Thus, our VCA analysis underscores the subtle interplay of geometric frustration, quantum fluctuations, and dimensionality, and elucidates the crucial role of short-range correlations in stabilizing and competing ground states of frustrated quantum magnets.
We propose a generalized Shastry-Sutherland model which bridges the Shastry-Sutherland model and the
J1-
J2 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
J1-
J2 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.
We study the ground-state phase diagram of the Shastry-Sutherland model by using a variational optimization of the infinite tensor network states, and identify a weakly first-order transition between the plaquette valence bond solid and the antiferromagnetic states. The full plaquette state is found to strongly compete with the empty plaquette ground state, and can be stabilized as the ground state when a staggered ring-exchange interaction preserving the Shastry-Sutherland lattice symmetry is introduced. We propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point (DQCP). The analysis of susceptibilities provides evidence of an emergent
SO(5) symmetry at this point. These results shed light on the study of DQCP in quantum magnets and provide a way to understand the proximate DQCP signatures in recent experiments on
SrCu2(BO3)2.