Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality

Abstract: 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.