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 $\text{SO}(5)$ 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 ${\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}$.
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.
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}.
Frustrated quantum magnets can host a variety of exotic spin excitations, including fractionalized spin excitations coupled to emergent gauge fields at deconfined quantum critical points (DQCPs) and chiral magnons in altermagnets. Here, we investigate the spin excitation spectra of the highly frustrated S=1/2 antiferromagnetic (AFM) Shastry-Sutherland model, focusing on the evolution of low-energy collective modes from the Néel AFM phase to the plaquette valence bond solid (PVBS). We demonstrate that the AFM state exhibits altermagnetic behavior, characterized by a non-relativistic splitting between two chiral magnon bands. Furthermore, we identify two additional low-energy excitations: a Higgs mode in the longitudinal excitation channel and an S=0 excitation with vanishing spectral weight. As the system approaches the AFM-to-PVBS transition, both these modes soften along with the lowest-energy triplet and singlet modes in the PVBS state. The closing gap of the Higgs mode, combined with the nearly degenerate velocities of S=1 and S=0 excitations, provides spectral evidence that the AFM-to-PVBS transition is proximate to a DQCP with emergent O(4) symmetry. Our results help clarify the spectral signature of a broad class of symmetry enhanced quantum phase transitions including deconfined quantum criticality.
The deconfined quantum critical point (DQCP) has become a central open concept in the physics of quantum matter, and its proposed presence in the Shastry-Sutherland model was followed by the experimental observation of at least a minimal DQC scenario induced by an applied magnetic field in SrCu2(BO3)2. However, the nature of the plaquette-singlet phase in SrCu2(BO3)2 remains unresolved, and with it the identification of the DQCP symmetry from among several theoretical scenarios. Here we perform detailed high-pressure 11B NMR studies to reveal the presence of both the full-plaquette (FP) and empty-plaquette (EP) phases in SrCu2(BO3)2, phase-separated at a first-order, pressure-driven transition with a volume-fraction effect. The field-driven transition from the EP to the antiferromagnetic (AFM) phase complements our previous observations of the FP--AFM transition, with both showing deconfined quantum criticality, while the scaling of the spin-lattice relaxation rate near the EP--AFM transition, 1/T1∝T0.6, suggests a DQCP governed by a different universality class. We discuss possible extensions to the Shastry-Sutherland model that account for these pressure and field effects. The expanded phase space we discover mandates an SO(5) DQCP symmetry, and hence our results take an important step towards a complete understanding of deconfined quantum criticality in SrCu2(BO3)2.
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 SrCu2(BO3)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.
Abstract Deconfined quantum critical points (DQCPs) have been proposed as a class of continuous quantum phase transitions occurring between two ordered phases with distinct symmetry-breaking patterns, beyond the conventional framework of Landau-Ginzburg-Wilson (LGW) theory. At the DQCP, the system exhibits emergent gauge fields, fractionalized excitations, and enhanced symmetries. Here we review recent theoretical and experimental progress on exploring DQCPs in condensed matter systems. We first introduce theoretical advancements in the study of DQCPs over the past twenty years, particularly in magnetic models on square lattices, honeycomb lattices, kagome lattices, and one-dimensional spin chains. We then discuss recent progress on experimental realization of DQCP in quantum magnetic systems. Experimentally, the Shastry-Sutherland model, realized in SrCu2(BO3)2, offers a particularly promising platform for realizing DQCPs. The magnetic frustration inherent to this model drives phase transitions between two distinct symmetry-breaking states: a valence bond solid (VBS) phase and a Néel antiferromagnetic phase. Remarkably, SrCu2(BO3)2 has provided the first experimental evidence of a proximate DQCP through a field-induced Bose-Einstein condensation, transitioning from the VBS state to the Néel state. Nevertheless, the direct experimental realization of a DQCP remains a significant challenge. Despite this, it offers a promising platform for exploring emergent phenomena through quantum phase transition in low-dimensional quantum systems.
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.