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

TL;DR

This paper provides numerical evidence that the quantum critical point between Ne9el and valence-bond-solid phases exhibits an emergent SO(5) symmetry, suggesting a continuous phase transition with novel conformal field theory properties.

Contribution

It demonstrates the emergence of SO(5) symmetry at the Ne9el to valence-bond-solid transition in a 2+1D lattice model, revealing new insights into deconfined quantum criticality.

Findings

Emergent SO(5) symmetry at the critical point.

Supports the transition being truly continuous.

Implications for a novel conformal field theory in 3D.

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.