## 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 (J_{1}≡ 1) 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-½ 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 J_{2}^{c}= ½ (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 (Δ → ∞), J_{2}^{c}→ 0.5 as expected.Original language | English |
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Article number | 415213 (11pp) |

Journal | Journal of Physics: Condensed Matter |

Volume | 20 |

DOIs | |

Publication status | Published - 2008 |

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_{1}

^{XXZ}-

*J*

_{2}

^{XXZ }model on the square lattice'. Together they form a unique fingerprint.