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We outline how the coupled cluster method of microscopic quantum many-bodytheory can be utilized in practice to give highly accurate results for theground-state properties of a wide variety of highly frustrated and stronglycorrelated spin-lattice models of interest in quantum magnetism, includingtheir quantum phase transitions. The method itself is described, and it isshown how it may be implemented in practice to high orders in a systematicallyimprovable hierarchy of (so-called LSUB$m$) approximations, by the use ofcomputer-algebraic techniques. The method works from the outset in thethermodynamic limit of an infinite lattice at all levels of approximation, andit is shown both how the "raw" LSUB$m$ results are themselves generallyexcellent in the sense that they converge rapidly, and how they may accuratelybe extrapolated to the exact limit, $m \rightarrow \infty$, of the truncationindex $m$, which denotes the {\it only} approximation made. All of this isillustrated via a specific application to a two-dimensional, frustrated,spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on a honeycomb lattice withnearest-neighbor and next-nearest-neighbor interactions with exchange couplings$J_{1}>0$ and $J_{2} \equiv \kappa J_{1} > 0$, respectively, where bothinteractions are of the same anisotropic $XXZ$ type. We show how the method canbe used to determine the entire zero-temperature ground-state phase diagram ofthe 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.

Highly frustrated spin-lattice models of magnetism and their quantum phase transitions: A microscopic treatment via the coupled cluster method