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The European Physical Journal B

Optimal coupled-cluster approximation for the ground-state properties of a spin-boson model

W.H. Wong, Chi‐Fai Lo

Published Nov 1, 1998• 4 citations
Publisher
DOI
10.1007/s100510050544

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In this work we have applied the optimal coupled-cluster approximation to study the ground state of the E⊗(b1+b2) Jahn–Teller effect. The effectiveness of the optimal coupled-cluster approximation has been investigated for the whole range of the asymmetry parameter and various coupling strengths. It is shown that our results up to the third level of approximation are in very good agreement with the exact numerical diagonalization results and are better than those from earlier variational treatments. Furthermore, unlike previous variational treatments, the optimal coupled-cluster approximation has the advantage that the accuracy of both the ground state energy and wavefunction estimates is being taken care of and can be systematically improved. Since the mathematical treatment in this work is simple, the optimal coupled-cluster approximation could be easily extended to the studies of other fermion-boson interacting systems, e.g. the extended Jahn–Teller system.
The spontaneous dimerization of frustrated spin- 1/2 antiferromagnetic chains is studied via a microscopic approach based on a proper set of composite operators (i.e., pseudo-spin operators). Two approximation schemes are developed. Firstly, a spin-wave approximation is made via a Dyson-Maleev-like boson transformation. The ground-state properties and the triplet excitation spectra are obtained as functions of the coupling parameter. Secondly, a microscopic treatment, based on pseudo-spin operators, is formulated within the framework of the powerful, systematic coupled-cluster method (CCM). Comparison between various approximations is made. The advantage of the CCM for the purposes of systematic improvement is emphasized.
The coupled cluster method (CCM) is applied to the spin-half XXZ model on the honeycomb lattice. Hierarchical CCM approximation schemes are applied in order to obtain the ground-state properties. The possible critical behavior of this model is also examined. Reasonably good results for the ground-state energy and the staggered magnetization are obtained, in comparison to the results from Monte Carlo simulations, spin-wave techniques, series expansions, and finite lattice diagonalizations, that have already been performed on this model.