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 x_c1 ≈ 0.207(3), x_c2 ≈ 0.385(10) and x_c3 ≈ 0.65(5). The transitions at x_c1 and x_c3 appear to be continuous (and hence deconfined) ones, while that at x_c2 appears to be a direct first-order one.