A frustrated spin-1 J_1-J_2 Heisenberg antiferromagnet:An anisotropic planar pyrochlore model

摘要

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 ≡ К 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 К_(c1) ≈ 1.00 ± 0.01 (as does the classical model at К_(c1) = 1) between two antiferromagnetic phases, viz., a quasiclassical Néel phase (for К < К_(c1)) and one of the infinitely degenerate family of quasiclassical phases (for К >К_(c1)) that exists in the classical model for К>К_(cl), which is now chosen by the order by disorder mechanism as (probably) the "doubled Néel" (or Néel~*) 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 К_(c2) ≈ 2.0± 0.5 in the spin-1 model, such that for К> К_(c2) the quasiclassical (Néel~*) 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 Néel 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 К>К_(c2).