## Abstract

We study the zero-temperature phase diagram of the J_{1} ^{XXZ}-J_{2} ^{XXZ} Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour () and next-nearest-neighbour (J_{2}>0) bonds. The two bonds have the same XXZ-type anisotropy in spin space. The effects on the quasiclassical Néel-ordered and collinear stripe-ordered states of varying the anisotropy parameter Δ are investigated using the coupled cluster method carried out up to high orders. By contrast with the case for spin- particles studied previously, no intermediate disordered phase between the Néel and collinear stripe phases, for any value of the frustration J_{2}/J _{1}, for either the z-aligned (Δ>1) or xy-planar-aligned (0≤Δ<1) states, is predicted here. The quantum phase transition is determined as first order for all values of J_{2}/J_{1} and Δ. The position of the phase boundary J_{2} ^{c}(Δ) is determined accurately. It is observed to deviate most from its classical position (for all values of Δ>0) at the Heisenberg isotropic point (Δ = 1), where J_{2} ^{c}(1) = 0.55 ± 0.01. By contrast, at the XY isotropic point (Δ = 0), we find J_{2} ^{c}(0) = 0.50 ± 0.01. In the Ising limit (), as expected.

Original language | English (US) |
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Article number | 415213 |

Journal | Journal of Physics Condensed Matter |

Volume | 20 |

Issue number | 41 |

DOIs | |

State | Published - Oct 15 2008 |