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

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 N'eel antiferromagnetic (AFM) phase for $\kappa < \kappa_{c_{1}} \approx 0.47$,acollinearstripedAFMphasefor$\kappa > \kappa_{c_{2}} \approx 0.60$,andaparamagneticPVBCphasefor$\kappa_{c_{1}} \lesssim \kappa \lesssim \kappa_{c_{2}}$\mathrm{.}Thetransitionat$\kappa_{c_{2}}$appearstobeoffirst-ordertype,whilethatat$\kappa_{c_{1}}$ is continuous. Since the N'eel and PVBC phases break different symmetries our results favor the deconfinement scenario for the transition at ${\kappa }_{c_1}$.