Valence-bond crystalline order in the s = 1/2 J1-J2 model on the honeycomb lattice.

Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbour exchange coupling J1 > 0 and frustrating next-nearest-neighbour coupling J2 ≡ xJ1 > 0. In the range 0 < x < 1 we find four phases exhibiting respectively Néel, 6-spin plaquette, staggered dimer and Néel-II orderings, with quantum critical points at xc1 ≈ 0.207(3), xc2 ≈ 0.385(10) and xc3 ≈ 0.65(5). The transitions at xc1 and xc3 appear to be continuous (and hence deconfined) ones, while that at xc2 appears to be a direct first-order one.