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

We study the zero-temperature ground-state (GS) properties of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore, using the coupled cluster method (CCM) implemented to high orders of approximation. The system comprises a J ₁–J ₂ model on the checkerboard lattice, with isotropic Heisenberg interactions of strength J ₁ between all nearest–neighbour pairs of spins on the square lattice, and of strength J ₂ between half of the next-nearest–neighbour pairs (in the checkerboard pattern). We calculate results for the GS energy and average local GS on-site magnetization, using various antiferromagnetic classical ground states as CCM model states. We also give results for the susceptibility of one of these states against the formation of crossed-dimer valence-bond crystalline (CDVBC) ordering. The complete GS phase diagram is presented for arbitrary values of the frustration parameter $\kappa \equiv J_2/J_1$, and when each of the exchange couplings can take either sign. (paper)