The frustrated Heisenberg antiferromagnet on the honeycomb lattice: A candidate for deconfined quantum criticality

Abstract

We study the ground-state (gs) phase diagram of the frustrated spin-1/2 $J_1$-$J_2$-$J_3$ antiferromagnet with $J_2=J_3=\kappa J_1$ on the honeycomb lattice, using coupled-cluster theory and exact diagonalization methods. We present results for the gs energy, magnetic order parameter, spin-spin correlation function, and plaquette valence-bond crystal (PVBC) susceptibility. We find a Néel antiferromagnetic (AFM) phase for $\kappa <{\kappa }_{c_1}\approx 0.47$, a collinear striped AFM phase for $\kappa >{\kappa }_{c_2}\approx 0.60$, and a paramagnetic PVBC phase for ${\kappa }_{c_1}\lesssim \kappa \lesssim {\kappa }_{c_2}$. The transition at ${\kappa }_{c_2}$ appears to be of first-order type, while that at ${\kappa }_{c_1}$ is continuous. Since the Néel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at ${\kappa }_{c_1}$.

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