  We investigate the ground-state phase diagram of an anisotropic Heisenberg
model on the honeycomb lattice with competing interactions. We use quantum
Monte Carlo simulations, as well as linear spin-wave and Ising series
expansions, to determine the phase boundaries of the ordered magnetic phases.
We find a region without any classical order in the vicinity of a highly
frustrated point. Higher-order correlation functions in this region give no
signal for long-range valence-bond order. The low-energy spectrum is derived
via exact diagonalization to check for topological order on small-size periodic
lattices.
