We propose a generalized Shastry-Sutherland (SS) model which bridges the SS model and the $J_1\text{−}{J}_2$ 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 Néel antiferromagnetic (AFM) phase in the pure SS model is a weak first one. This result indicates the existence of an exotic tricritical point in the pVBS to AFM transition line in the phase diagram, as the transition in the $J_1\text{−}{J}_2$ Heisenberg model was previously determined to be continuous. We determine the location of the tricritical point in the phase diagram at which the first-order transition turns continuous. Our generalized SS model provides not only a valuable platform to explore exotic phases and phase transitions but also more realistic description of SS materials like ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$.

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• Frustrated magnetism
• Magnetic phase transitions
• Valence bond solid
• Density matrix renormalization group
• Tensor network methods