The frustrated Heisenberg antiferromagnet on the honeycomb lattice: J ₁-J ₂ model

We study the ground-state phase diagram of the frustrated spin-1/2J ₁-J ₂ antiferromagnet with J ₂ = xJ ₁ > 0 (J ₁ > 0) on the honeycomb lattice, using the coupled-cluster method. We present results for the ground-state energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. We find a paramagnetic PVBC phase for x _c1 < x < x _c2, where x _c1 ≈ 0.207 ± 0.003 and x _c2 ≈ 0.385 ± 0.010. The transition at x _c1 to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range 0.21 ≲ x ≲ 0.24), while that at x _c2 is of first-order type to another quasiclassical antiferromagnetic phase that occurs in the classical version of the model only at the isolated and highly degenerate critical point x = 1/2 . The spiral phases that are present classically for all values x > 1/6 are absent for all x ≲ 1.