Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition

Journal article

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.

Authors: Nahum, A; Serna, P; Chalker, J; Ortuño, M; Somoza, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review Letters
• Volume: 115
• Issue: 26
• Article number: 267203
• Publication date: 2015-12-23
• DOI: 10.1103/physrevlett.115.267203
• EISSN: 1079-7114
• ISSN: 0031-9007
• Pmid: 26765019
• Language: English
• Keywords: SBTMR