High-order coupled cluster method calculations for the ground- and excited-state properties of the spin-half<i>XXZ</i>model

Abstract

In this article, we present new results of high-order coupled cluster method\n(CCM) calculations, based on a N\\'eel model state with spins aligned in the\n$z$-direction, for both the ground- and excited-state properties of the\nspin-half {\\it XXZ} model on the linear chain, the square lattice, and the\nsimple cubic lattice. In particular, the high-order CCM formalism is extended\nto treat the excited states of lattice quantum spin systems for the first time.\nCompletely new results for the excitation energy gap of the spin-half {\\it XXZ}\nmodel for these lattices are thus determined. These high-order calculations are\nbased on a localised approximation scheme called the LSUB$m$ scheme in which we\nretain all $k$-body correlations defined on all possible locales of $m$\nadjacent lattice sites ($k \\le m$). The ``raw'' CCM LSUB$m$ results are seen to\nprovide very good results for the ground-state energy, sublattice\nmagnetisation, and the value of the lowest-lying excitation energy for each of\nthese systems. However, in order to obtain even better results, two types of\nextrapolation scheme of the LSUB$m$ results to the limit $m \\to \\infty$ (i.e.,\nthe exact solution in the thermodynamic limit) are presented. The extrapolated\nresults provide extremely accurate results for the ground- and excited-state\nproperties of these systems across a wide range of values of the anisotropy\nparameter.\n