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

Physical Review Letters
Adam NahumA M Somoza

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.

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Citations

Dec 9, 2017·Physical Review Letters·Toshihiro SatoFakher F Assaad
Sep 20, 2019·Nature Communications·Xue-Yang SongYin-Chen He
Jul 11, 2018·Proceedings of the National Academy of Sciences of the United States of America·Snir GazitChong Wang
May 20, 2017·Physical Review Letters·Jonathan D'Emidio, Ribhu K Kaul
Mar 31, 2018·Physical Review Letters·Xue-Feng ZhangFrank Pollmann
May 21, 2019·Physical Review Letters·Nvsen MaZi Yang Meng
Oct 8, 2016·Physical Review Letters·Yu Nakayama, Tomoki Ohtsuki
Jan 9, 2021·Physical Review Letters·Bowen ZhaoAnders W Sandvik
Jan 21, 2021·Physical Review. E·Claudio BonatiEttore Vicari
Feb 13, 2021·Physical Review Letters·Zhenjiu WangFakher F Assaad
May 7, 2021·Science Advances·Eslam KhalafAshvin Vishwanath

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