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Physical review. B, Condensed matter

Many-body correlations in quantum antiferromagnets: A microscopic coupled-cluster approach

R. F. Bishop, John B. Parkinson, Yang Xian

Published Jun 1, 1991• 59 citations
Publisher

Abstract

The coupled-cluster method of many-body theory is applied to anisotropic quantum antiferromagnets in one and two dimensions. It is found to give good results for ground-state and excited-state energies and the staggered magnetization. It also gives a qualitatively correct description of the entire one-dimensional Heisenberg-Ising phase and the phase change in one dimension as the anisotropy decreases.

DOI
10.1103/physrevb.43.13782

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The coupled-cluster method of many-body theory is applied to anisotropic quantum antiferromagnets in one and two dimensions. It is found to give good results for ground-state and excited-state energies and the staggered magnetization. It also gives a qualitatively correct description of the entire one-dimensional Heisenberg-Ising phase and the phase change in one dimension as the anisotropy decreases.
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.
The coupled-cluster method (CCM) has already been successfully applied by us to anisotropic quantum antiferromagnetic models (XXZ model) with spin s=1/2 in one and two dimensions. This approach is now generalized to the same models but with spin s>1/2. We mainly consider the one-dimensional system in this article. Several systematic approximation schemes developed previously are employed. The ground-state energy is obtained as a function of the spin s and anisotropy. It is found that, for a given approximation that contains long-range contributions, the critical value of the anisotropy for the Heisenberg-Ising phase transition rapidly approaches the classical value of 1 as the spin s increases. We also generalize one of the schemes to a hypercubic lattice of arbitrary dimensionality. By making a detailed comparison with spin-wave theory, perturbation theory, and other variational approaches, some additional intrinsic features of the CCM treatments are emphasized.
We extend our own previous applications of the microscopic coupled-cluster method (CCM) to quantum antiferromagnets. In particular, we carry out a systematic calculation involving high-order multispin correlations for the spin-1/2 anisotropic Heisenberg models on the one-dimensional chain and the two-dimensional square lattice. Their ground-state properties are obtained as functions of the anisotropy parameter. Our CCM analysis not only produces accurate results for such physical quantities as the ground-state energy which are comparable to the best results from other techniques, but it also enables us to study the quantum phase transitions of the spin models in a systematic and unbiased manner. © 1996 John Wiley & Sons, Inc.
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.
Strongly interacting quantum spin–lattice models exhibit a wide variety of phases with diverse and subtle magnetic ordering properties. Their detailed description within a unified microscopic framework poses a real challenge for the many-body theorist. By specific application to the spin-½ anisotropic Heisenberg model on a square lattice, we show how the ab initio coupled cluster method, which has already been very successfully applied to a wide variety of quantum many-body and field-theoretic systems, may be very efficiently and systematically implemented for spin–lattice models. Results for such local properties as the ground-state energy and sublattice magnetization are thereby obtained which are on a par with those from the best of the available alternative methods. Furthermore, we demonstrate explicitly how the coupled cluster method now also provides an effective and fully microscopic tool to yield systematic and accurate estimates of the zero-temperature quantum phase transition boundaries between states of different quantum order, as well as of the critical behaviour of the system in the vicinity of the transition points.
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.