Coplanar order induced by emergent frustration

Traditional frustration arises from the conflict between the spin alignments due to the geometry or the nature of the interactions. Here, we demonstrate a novel form of frustration, dubbed ``emergent frustration'', which is induced by the symmetry that emerges at the phase transition point of a quantum spin model devoid of geometric frustration. We study the two-dimensional bipartite chequerboard $J$-$Q$ model, which hosts the antiferromagnetic (AFM) state to the plaquette-singlet solid state (PSS) phase transition detected in the Shastry-Sutherland compound SrCu$_2({\rm BO}_3)_2$. By analyzing the scaling behavior of the R\'enyi entanglement entropy with smooth boundaries at the transition point, we observe an unexpected scaling behavior, which indicates that the number of Goldstone modes is five. We explain this by proposing a novel scenario in which the system is described by an effective quantum rotor Hamiltonian with a three-sublattice geometry that frustrates collinear order while supporting coplanar order. Such a three-sublattice geometry arises from the emergent symmetry of coexisting orders, which may also occur at the AFM-PSS transition point of SrCu$_2({\rm BO}_3)_2$. Therefore, experimental investigations are warranted.