A frustrated spin-1 J1-J2 Heisenberg antiferromagnet: An anisotropic planar pyrochlore model

The zero-temperature ground-state (GS) properties and phase diagram of a frustrated spin-1 J(1)-J(2) Heisenberg model on the checkerboard square lattice are studied, using the coupled cluster method. We consider the case where the nearest-neighbour exchange bonds have strength J(1) > 0 and the next-nearest-neighbour exchange bonds present (viz., in the checkerboard pattern of the planar pyrochlore) have strength J(2) kappa J(1) > 0. We find significant differences from both the spin-1/2 and classical versions of the model. We find that the spin-1 model has a first phase transition at kappa(c1) approximate to 1.00 +/- 0.01 (as does the classical model at kappa(c1) = 1) between two antiferromagnetic phases, viz., a quasiclassical Neel phase (for kappa < kappa(c1)) and one of the infinitely degenerate family of quasiclassical phases (for kappa > kappa(c1)) that exists in the classical model for kappa > kappa(c1), which is now chosen by the order by disorder mechanism as (probably) the "doubled Neel" (or Neel") state. By contrast, none of this family survives quantum fluctuations to form a stable GS phase in the spin-1/2 case. We also find evidence for a second quantum critical point at kappa(c2) approximate to 2.0 +/- 0.5 in the spin-1 model, such that for kappa > kappa(c2) the quasiclassical (Neel*) ordering melts and a nonclassical phase appears, which, on the basis of preliminary evidence, appears unlikely to have crossed-dimer valence-bond crystalline (CDVBC) ordering, as in the spin-1/2 case. Unlike in the spin-1/2 case, where the Neel and CDVBC phases are separated by a phase with plaquette valence-bond crystalline (PVBC) ordering, we find very preliminary evidence for such a PVBC state in the spin-1 model for all kappa > kappa(c2).