Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J1-J2 model

We study the zero-temperature ground-state (gs) phase diagram of the spin-1/2 anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is equivalently described as a frustrated J(1)-J(2) antiferromagnet on the two-dimensional checkerboard lattice, with nearest-neighbor exchange bonds of strength J(1) > 0 and next-nearest-neighbor bonds of strength J(2) kappa J(1) > 0. Using various antiferromagnetic (AFM) classical ground states as CCM reference states, we present results for the gs energy, average local on-site magnetization, and the susceptibilities of these states against the formation of plaquette valence-bond crystal (PVBC) and crossed-dimer valence-bond crystal (CDVBC) ordering. We show that the AFM quasiclassical state with Neel ordering is the gs phase for kappa < kappa c(1) approximate to 0.80 +/- 0.01, but that none of the infinitely degenerate set of AFM states that form the gs phase for the classical version (s ->infinity) of the model (for kappa > 1) survive the quantum fluctuations to form a stable magnetically ordered gs phase for the s = 1/2 case. Instead, our calculations indicate a PVBC-ordered phase for kappa(c1) < kappa <kappa(c2) approximate to 1.22 +/- 0.02, and a CDVBC-ordered phase for all kappa > kappa(c2). Both transitions are likely to be direct ones, although we cannot exclude very narrow coexistence regions confined to 0.79 less than or similar to kappa less than or similar to 0.81 and 1.20 less than or similar to kappa less than or similar to 1.22, respectively.