Frustrated Heisenberg antiferromagnet on the checkerboard lattice: J(1)-J(2) model

We study the zero-temperature ground-state (gs) phase diagram of the spin-12 anisotropic planar pyrochlore (or crossed chain) model using the coupled cluster method (CCM). The model is equivalently described as a frustrated J1-J2 antiferromagnet on the two-dimensional checkerboard lattice, with nearest-neighbor exchange bonds of strength J1>0 and next-nearest-neighbor bonds of strength J2≡κJ1>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 Néel ordering is the gs phase for κ1) 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 κc1κc2. Both transitions are likely to be direct ones, although we cannot exclude very narrow coexistence regions confined to 0.79≲κ≲0.81 and 1.20≲κ≲1.22, respectively