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The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_{1}$--$J_{2}$ model

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_{1}$--$J_{2}$ antiferromagnet with $J_{2}=κJ_1>0$ ($J_{1}>0$) 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 $κ_{c_1}<κ<κ_{c_2}$, where $κ_{c_1} \approx 0.207 \pm 0.003$ and $κ_{c_2} \approx 0.385 \pm 0.010$. The transition at $κ_{c_1}$ to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range $0.21 \lesssim κ\lesssim 0.24$), while that at $κ_{c_2}$ 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 $κ= 1/2$. The spiral phases that are present classically for all values $κ> 1/6$ are absent for all $κ\lesssim 1$.