Weak plaquette valence bond order in the S=1/2 honeycomb J ₁-J₂ heisenberg model

Using the density matrix renormalization group, we investigate the S=1/2 Heisenberg model on the honeycomb lattice with first (J₁) and second (J₂) neighbor interactions. We are able to study long open cylinders with widths up to 12 lattice spacings. For J₂/J₁ near 0.3, we find an apparently paramagnetic phase, bordered by an antiferromagnetic phase for J₂â‰0.26 and by a valence bond crystal for J₂â‰0.36. The longest correlation length that we find in this intermediate phase is for plaquette valence bond order. This correlation length grows strongly with cylinder circumference, indicating either quantum criticality or weak plaquette valence bond order.