  We outline how the coupled cluster method of microscopic quantum many-body
theory can be utilized in practice to give highly accurate results for the
ground-state properties of a wide variety of highly frustrated and strongly
correlated spin-lattice models of interest in quantum magnetism, including
their quantum phase transitions. The method itself is described, and it is
shown how it may be implemented in practice to high orders in a systematically
improvable hierarchy of (so-called LSUB$m$) approximations, by the use of
computer-algebraic techniques. The method works from the outset in the
thermodynamic limit of an infinite lattice at all levels of approximation, and
it is shown both how the "raw" LSUB$m$ results are themselves generally
excellent in the sense that they converge rapidly, and how they may accurately
be extrapolated to the exact limit, $m \rightarrow \infty$, of the truncation
index $m$, which denotes the {\it only} approximation made. All of this is
illustrated via a specific application to a two-dimensional, frustrated,
spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on a honeycomb lattice with
nearest-neighbor and next-nearest-neighbor interactions with exchange couplings
$J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$, respectively, where both
interactions are of the same anisotropic $XXZ$ type. We show how the method can
be used to determine the entire zero-temperature ground-state phase diagram of
the model in the range $0 \leq \kappa \leq 1$ of the frustration parameter and
$0 \leq \Delta \leq 1$ of the spin-space anisotropy parameter. In particular,
we identify a candidate quantum spin-liquid region in the phase space.
