Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets

Recent experiments[Guo et al., Phys. Rev. Lett. 124 206602 (2020)] on thermodynamic properties of the frustrated layered quantum magnet SrCu₂(BO₃)₂—the Shastry-Sutherland material—have provided strong evidence for a low-temperature phase transition between plaquette-singlet and antiferromagnetic order as a function of pressure. Further motivated by the recently discovered unusual first-order quantum phase transition with an apparent emergent O(4) symmetry of the antiferromagnetic and plaquette-singlet order parameters in a two-dimensional "checkerboard J-Q" quantum spin model[Zhao et al., Nat. Phys. 15 678 (2019)], we here study the same model in the presence of weak inter-layer couplings. Our focus is on the evolution of the emergent symmetry as the system crosses over from two to three dimensions and the phase transition extends from strictly zero temperature in two dimensions up to finite temperature as expected in SrCu₂(BO₃)₂. Using quantum Monte Carlo simulations, we map out the phase boundaries of the plaquette-singlet and antiferromagnetic phases, with particular focus on the triple point where these two ordered phases meet the paramagnetic phase for given strength of the inter-layer coupling. All transitions are first-order in the neighborhood of the triple point. We show that the emergent O(4) symmetry of the coexistence state breaks down clearly when the interlayer coupling becomes sufficiently large, but for a weak coupling, of the magnitude expected experimentally, the enlarged symmetry can still be observed at the triple point up to significant length scales. Thus, it is likely that the plaquette-singlet to antiferromagnetic transition in SrCu₂(BO₃)₂ exhibits remnants of emergent O(4) symmetry, which should be observable due to additional weakly gapped Goldstone modes.