SO(5) multicriticality in two-dimensional quantum magnets

We resolve the nature of the quantum phase transition between a N\'eel antiferromagnet and a valence-bond solid in two-dimensional spin-1/2 magnets. We study a class of J-Q models, in which Heisenberg exchange J competes with interactions Qₙ formed by products of n singlet projectors on adjacent parallel lattice links. QMC simulations provide unambiguous evidence for first-order transitions, with the discontinuities increasing with n. For n=2 and n=3 models, the first-order signatures are very weak. On intermediate length scales, we extract well-defined scaling dimensions (critical exponents) that are common to the models with small n, indicating proximity to a quantum critical point. By combining two Q terms, the transition can be tuned from weak to more strongly first-order. The two coexisting orders on the first-order line scale with a large exponent 0. 85. This exponent and others are close to bounds for an SO (5) symmetric CFT with a relevant SO (5) singlet. We characterize the emergent SO (5) symmetry by the scaling dimensions of its leading irrelevant perturbations. The large value and a large correlation length exponent, 1. 4, partially explain why the transition remains near-critical even quite far away from the critical point and in many different models without fine-tuning. In addition, we find that few-spin lattice operators are dominated by the SO (5) violating field (the traceless symmetric tensor), and interactions involving many spins are required to observe strong effects of the relevant SO (5) singlet. The exponent that had previously been identified with the divergent correlation length when crossing between the two phases does not have a corresponding CFT operator. We explain this emergent pseudocritical scale by a mechanism relying on a dangerously irrelevant SO (5) perturbation.