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

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 \(\Delta=1\).