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We study the zero-temperature ($T=0$) ground-state (GS) properties of afrustrated spin-half $J^{XXZ}_{1}$--$J^{XXZ}_{2}$ model on the honeycomblattice with nearest-neighbor and next-nearest-neighbor interactions withexchange couplings $J_{1}>0$ and $J_{2} \equiv \kappa J_{1}>0$, respectively,using the coupled cluster method. Both interactions are of the anisotropic$XXZ$ type. We present the $T=0$ GS phase diagram of the model in the ranges $0\leq \Delta \leq 1$ of the spin-space anisotropy parameter and $0 \leq \kappa\leq 1$ of the frustration parameter. A possible quantum spin-liquid region isidentified.

Phase diagram of a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ $XXZ$ model on the honeycomb lattice