Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition
Author(s)Nahum, Adam; Serna, P.; Chalker, J. T.; Somoza, A. M.; Ortuno, M.
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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[subscript 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[superscript 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.
DepartmentMassachusetts Institute of Technology. Department of Physics
Physical Review Letters
American Physical Society
Nahum, Adam, P. Serna, J. T. Chalker, M. Ortuno, and A. M. Somoza. “Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition.” Physical Review Letters 115, no. 26 (December 23, 2015). © 2015 American Physical Society
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