Quantum Criticality with Emergent Symmetry in the Extended Shastry-Sutherland Model

Motivated by the novel phenomena observed in the layered material SrCu₂⁢(BO₃)₂, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for SrCu₂⁢(BO₃)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 SrCu₂⁢(BO₃)₂.

In the first part of this supplemental material, we first compare our tensor network results with QMC results for J-Q model, then we compare our Shastry-Sutherl(SS) model results with DMRG results and examine the convergence of bond dimensions. Finally we further compare our SS model results with previous iPEPS and iPESS results. In the second part, we examine the induced dimerized patterns with different types of open boundary conditions.