title: Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition.
abstract: We show numerically that the "deconfined" quantum critical point between the Néel 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 Néel 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)×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 CP(1) 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.
authors.affiliation: Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Adam
authors.initials: A
authors.lastname: Nahum
authors.affiliation: Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
authors.forename: P
authors.initials: P
authors.lastname: Serna
authors.affiliation: Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.
authors.forename: J T
authors.initials: JT
authors.lastname: Chalker
authors.affiliation: Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Ortuño
authors.affiliation: Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.
authors.forename: A M
authors.initials: AM
authors.lastname: Somoza