The frustrated Heisenberg antiferromagnet on the honeycomb lattice: $J_1$--$J_2$ model

Abstract

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_1$--$J_2$ antiferromagnet with $J_2=\kappa J_1>0$ ($J_1>0$) 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 ${\kappa }_{c_1}<\kappa <{\kappa }_{c_2}$, where ${\kappa }_{c_1}\approx 0.207\pm 0.003$ and ${\kappa }_{c_2}\approx 0.385\pm 0.010$. The transition at ${\kappa }_{c_1}$ to the Néel phase seems to be a continuous deconfined transition (although we cannot exclude a very narrow intermediate phase in the range $0.21\lesssim \kappa \lesssim 0.24$), while that at ${\kappa }_{c_2}$ 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 $\kappa =1/2$. The spiral phases that are present classically for all values $\kappa >1/6$ are absent for all $\kappa \lesssim 1$.

6 pages, 5 figures

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