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Coupled Cluster Method Calculations Of Quantum Magnets With Spins Of General Spin Quantum Number

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Abstract

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, $$s$$. This new general-$$s$$'' formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic {\it XXZ} models and for the one-dimensional spin-half/spin-one ferrimagnetic {\it XXZ} model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalisation group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetisation of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at $$\Delta=1$$. By contrast, extrapolated CCM results for the sublattice magnetisation of the spin-one antiferromagnet using this same scheme are seen to go to zero at $$\Delta \approx 1.2$$, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetisations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of $$\Delta$$, up to and including the Heisenberg point at $$\Delta=1$$.

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04 September 2003
cond-mat/0309099 10.1023/A:1015769622279