Phase Transition Of The Spin-One Square-Lattice Anisotropic Heisenberg Model (original) (raw)

The coupled cluster method (CCM) is applied to the spin-one anisotropic Heisenberg antiferromagnet (HAF) on the square lattice at zero temperature using a new high-order CCM ground-state formalism for general quantum spin number (s ≥ 1/2). The results presented constitute the first such application of this new formalism, and they are shown to be among the most accurate results for the ground-state energy and sublattice magnetisation of this model as yet determined. We "track" the solution to the CCM equations at a given level of approximation with respect to the anisotropy parameter, ∆, from the trivial Ising limit (∆ → ∞) down to a critical value ∆c, at which point this solution terminates. This behaviour is associated with a phase transition in the system, and hence a primary result of these high-order CCM calculations is that they provide an accurate and unbiased (i.e., ab initio) estimation of the position of the quantum phase transition point as a function of the anisotropy parameter. Our result is, namely, that this point occurs at (or slightly below) the isotropic Heisenberg point at ∆ = 1, for this model.

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