N\'eel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality

Understand

We study a spin-1/2 SU(2) model on the honeycomb lattice with nearest-neighbor antiferromagnetic exchange $J$ that favors N\'eel order, and competing 6-spin interactions $Q$ which favor a valence bond solid (VBS) state in which the bond-energies order at the "columnar" wavevector ${\mathbf K} = (2\pi/3,-2\pi/3)$.

• We present quantum Monte-Carlo evidence for a direct continuous quantum phase transition between N\'eel and VBS states, with exponents and logarithmic violations of scaling consistent with those at analogous deconfined critical points on the square lattice.
• Although this strongly suggests a description in terms of deconfined criticality, the measured three-fold anisotropy of the phase of the VBS order parameter shows unusual near-marginal behaviour at the critical point.