The effect of anisotropy on the ground-state magnetic ordering of the spin-1 quantum J1XXZ-J2XXZ model on the square lattice

R. F. Bishop, P. H Y Li, R. Darradi, J. Richter, C. E. Campbell

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    Abstract

    We study the zero-temperature phase diagram of the J1XXZ-J2XXZ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour (J1 ≡ 1) and next-nearest-neighbour (J2 > 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 J2/J1, 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 J2/J1 and Δ. The position of the phase boundary J2c(Δ) is determined accurately. It is observed to deviate most from its classical position J2c = ½ (for all values of Δ > 0) at the Heisenberg isotropic point (Δ = 1), where J2c(1) = 0.55 ± 0.01. By contrast, at the XY isotropic point (Δ = 0), we find J2c(0) = 0.50 ± 0.01. In the Ising limit (Δ → ∞), J2c → 0.5 as expected.
    Original languageEnglish
    Article number415213 (11pp)
    JournalJournal of Physics: Condensed Matter
    Volume20
    DOIs
    Publication statusPublished - 2008

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