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Abstract:

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 þ 1)-dimensional analogue of the SOð4Þ¼½SUð2Þ × SUð2Þ=Z2 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 þ 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.