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We study the zero-temperature ground-state (GS) properties of thespin-$\frac{1}{2}$ anisotropic planar pyrochlore, using the coupled clustermethod (CCM) implemented to high orders of approximation. The system comprisesa $J_{1}$--$J_{2}$ model on the checkerboard lattice, with isotropic Heisenberginteractions of strength $J_{1}$ between all nearest-neighbour pairs of spinson the square lattice, and of strength $J_{2}$ between half of thenext-nearest-neighbour pairs (in the checkerboard pattern). We calculateresults for the GS energy and average local GS on-site magnetization, usingvarious antiferromagnetic classical ground states as CCM model states. We alsogive results for the susceptibility of one of these states against theformation of crossed-dimer valence-bond crystalline (CDVBC) ordering. Thecomplete GS phase diagram is presented for arbitrary values of the frustrationparameter $\kappa \equiv J_{2}/J_{1}$, and when each of the exchange couplingscan take either sign.

Ground-state phase structure of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore