Emergent SO(5) Symmetry at the Neel to Valence-Bond-Solid Transition

We show numerically that the deconfined quantum critical point between the Neel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Neel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2 + 1)-dimensional analogue of the SO(4) = [SU(2) x SU(2)]/Z(2) symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2 + 1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP1 model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.