Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal Formation

We present a comprehensive computational study of the phase diagram of the frustrated $S=1/2$ Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest $(J_2)$ and third-neighbor $(J_3)$ couplings. Using a combination of exact diagonalizations of the original spin model, of the Hamiltonian projected into the nearest neighbor short range valence bond basis, and of an effective quantum dimer model, we determine the boundaries of several magnetically ordered phases in the region $J_2,J_3\in [0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a {\em plaquette} valence bond crystal phase.