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arXiv · 1508.06668

Emergent $SO(5)$ Symmetry at the N\'eel to Valence-Bond-Solid Transition

Adam Nahum·P. Serna·J. T. Chalker·M. Ortuño·A. M. Somoza
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Abstract

We show numerically that the `deconfined' quantum critical point between the N\'eel antiferromagnet and the columnar valence-bond-solid, for a square lattice of spin-1/2s, has an emergent $SO(5)$ symmetry. This symmetry allows the N\'eel vector and the valence-bond-solid order parameter to be rotated into each other. It is a remarkable 2+1-dimensional analogue of the $SO(4)= [SU(2)\times SU(2)]/Z_2$ symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent $SO(5)$ is strong evidence that the phase transition in the 2+1D 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 (non-compact $CP^1$ model). The result indicates that in three dimensions there is an $SO(5)$-symmetric conformal field theory which has no relevant singlet operators, so is radically different to conventional Wilson-Fisher-type conformal field theories.

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Adam Nahum, P. Serna, J. T. Chalker, M. Ortuño, A. M. Somoza. 2015-08-26. Emergent $SO(5)$ Symmetry at the N\'eel to Valence-Bond-Solid Transition. https://doi.org/10.1103/physrevlett.115.267203

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