Coupled cluster method calculations of quantum magnets with spins of general spin quantum number

D. J J Farnell, R. F. Bishop, K. A. Gernoth

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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 XXZ models and for the one-dimensional spin-half/spin-one ferrimagnetic 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 renormalization group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetization of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at Δ = 1. By contrast, extrapolated CCM results for the sublattice magnetization of the spin-one antiferromagnet using this same scheme are seen to go to zero at Δ ≈ 1.2, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetizations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of Δ, up to and including the Heisenberg point at Δ = 1.
    Original languageEnglish
    Pages (from-to)401-428
    Number of pages28
    JournalJournal of Statistical Physics
    Volume108
    DOIs
    Publication statusPublished - 2002

    Keywords

    • CCM
    • Phase transitions
    • Quantum magnets

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