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Physical review. B, Condensed matter

Coupled-cluster approximation for a spin-1 Heisenberg antiferromagnet with anisotropic exchange interaction and easy-plane single-ion anisotropy

W. H. Wong, Chi‐Fai Lo, Y. L. Wang

Published Sep 1, 1994• 25 citations
Publisher

Abstract

In this paper we have applied the coupled-cluster method to investigate the ground state of the spin-1 Heisenberg antiferromagnet with anisotropic exchange interaction and easy-plane single-ion anisotropy. A coupled-cluster approximation up to the second level has been performed to evaluate the ground-state energy and staggered magnetization for various lattices such as linear chain, honeycomb, square, simple cubic, and body-centered-cubic lattice. The convergence of our results is fairly rapid, and thus the coupled-cluster method seems to be a practical tool for calculating ground-state energy of a spin system since only the first few levels of approximation will be needed in actual practice.

DOI
10.1103/physrevb.50.6126

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In this paper we have applied the coupled-cluster method to investigate the ground state of the spin-1 Heisenberg antiferromagnet with anisotropic exchange interaction and easy-plane single-ion anisotropy. A coupled-cluster approximation up to the second level has been performed to evaluate the ground-state energy and staggered magnetization for various lattices such as linear chain, honeycomb, square, simple cubic, and body-centered-cubic lattice. The convergence of our results is fairly rapid, and thus the coupled-cluster method seems to be a practical tool for calculating ground-state energy of a spin system since only the first few levels of approximation will be needed in actual practice.
Using the coupled-cluster method we investigate the ground-state properties of an easy-plane spin-one antiferromagnet which has a critical point at zero temperature. This spin system represents a nontrivial system with the single-ion anisotropy. Single-ion anisotropies have a fundamental influence on the behavior of a magnetic system, and prevail in almost all physical systems with spin greater than one half. Because of the complexities caused by the single-ion anisotropy term, the mean-field approximation is commonly used in calculations of the thermodynamic quantities. However, in the mean-field approximation both quantum and spin fluctuation correlations have been neglected. Here we apply the coupled-cluster method to obtain the ground-state energy, staggered magnetization and critical point for both two and three dimensional lattices. In the coupled-cluster method the correlations of the quantum and spin fluctuations have been systematically included.
A high-order coupled cluster method (CCM) for the zero-temperature ground states of quantum lattice spin systems of general spin quantum number (s> 1/2)(s>~1/2)(s> 1/2) is described and illustrated via the spin-1 anisotropic Heisenberg antiferromagnet on the square lattice. Results for the ground-state energy and sublattice magnetization are seen to be in excellent agreement with the best of other approximate methods. Furthermore, we are able to follow the solution to the CCM equations at a given level of approximation with respect to the anisotropy parameter $\ensuremath{\Delta}$ from the trivial Ising limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}\ensuremath{\infty})$ down to a critical value ${\ensuremath{\Delta}}_{c},$ at which point the physical solution terminates. The results for the ground-state energy, sublattice magnetization, and phase transition point thus support our choice of this model as a good nontrivial test case of our CCM formalism.
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≥1/2s \ge 1/2s≥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, ΔΔΔ, from the trivial Ising limit (Δ→∞Δ\to \inftyΔ→∞) down to a critical value ΔcΔ_cΔc​, 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., {\it 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 Δ=1Δ=1Δ=1, for this model.
The coupled-cluster method (CCM) is applied to anisotropic-quantum-antiferromagnetic models in one and two dimensions (1D and 2D). Several hierarchical approximation schemes of the CCM are defined, which are specialized for the spin-lattice models. Good results are obtained for both ground-state and excited-state energies. The spin-spin correlation functions and the staggered magnetizations are also calculated. We have found that the CCM gives a qualitatively correct description of the entire Heisenberg-Ising phase, including the critical point where a phase transition occurs in 1D. Some interesting differences between 1D and 2D models near the critical point are discussed.
We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the S=1S=1S=1 Heisenberg antiferromagnet with easy-axis or easy-plane single-site anisotropy on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared to spin-wave theory.