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 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 N´eel ordering is the gs phase for κ < κ_c1
≈ 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 →∞) of the model (for κ > 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 κ_c1 < κ < κc2 ≈ 1.22 ± 0.02, and a CDVBC-ordered phase for all κ > κ_c2 . 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.