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

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Using the coupled cluster method we study the phase diagram of the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice with nearest-neighbor exchange coupling J₁>0 and frustrating next-nearest-neighbor 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.