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

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arxiv 1508.06668 v1 pith:MVOY47QR submitted 2015-08-26 cond-mat.str-el cond-mat.stat-mechhep-th

Adam Nahum , P. Serna , J. T. Chalker , M. Ortuño , A. M. Somoza This is my paper · ORCID
classification cond-mat.str-elcond-mat.stat-mechhep-th
keywords symmetryemergenttransitionvalence-bond-solidconformalcriticalfieldmodel
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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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Cited by 4 Pith papers

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    Tensor networks demonstrate DQCP stability in the 1D spin-phonon model only for high phonon frequencies, with a first-order transition below a critical value whose endpoint belongs to the four-state Potts universality class.

  2. Bootstrapping the Simplest Deconfined Quantum Critical Point

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    Conformal bootstrap bounds for U(1)-charged scalars in 3d are saturated by the CP^2 model's large-N and lattice predictions, suggesting the CP^2 deconfined quantum critical point is a conformal field theory.

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    The notes argue that the FL* state — small pockets plus a quantized spin-liquid anomaly — resolves the ADMR pocket and v_F >> v_Delta problems that defeated holon-metal and plain fermionic-parton theories of the cuprates.

  4. Fractionalized Fermi liquids and the cuprate phase diagram

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