High-order coupled cluster method calculations for the ground- and excited-state properties of the spin-halfXXZmodel

Abstract

In this article, we present new results of high-order coupled cluster method (CCM) calculations, based on a Néel model state with spins aligned in the z-direction, for both the ground-and excitedstate properties of the spin-half XXZ model on the linear chain, the square lattice, and the simple cubic lattice. In particular, the high-order CCM formalism is extended to treat the excited states of lattice quantum spin systems for the first time. Completely new results for the excitation energy gap of the spin-half XXZ model for these lattices are thus determined. These high-order calculations are based on a localised approximation scheme called the LSUBm scheme in which we retain all k-body correlations defined on all possible locales of m adjacent lattice sites (k ≤ m).The "raw" CCM LSUBm results are seen to provide very good results for the ground-state energy, sublattice magnetisation, and the value of the lowest-lying excitation energy for each of these systems. However, in order to obtain even better results, two types of extrapolation scheme of the LSUBm results to the limit m → ∞ (i.e., the exact solution in the thermodynamic limit) are presented. The extrapolated results provide extremely accurate results for the ground-and excited-state properties of these systems across a wide range of values of the anisotropy parameter.

High-order coupled cluster calculations via parallel processing: An illustration forCaV4O9

“…2 shows LSUBm ground-state energy plotted against m −2 for m = {4, 6, 8, 10}. "Linear extrapolations" of data points have previously been used to great effect for isotropic nearest-neighbor antiferromagnets [2,3,4,5,6]. In this case of the CAVO model studies here, we obtain a value of E g /N = −0.55310 (5).…”

“…Our best results for the ground-state energy and sublattice magnetization for the pure nearest-neighbor model are given by Eg/N = −0.5534 and M = 0.19, respectively, and we predict that there is no Néel ordering in the region 0.2 ≤ J2/J1 ≤ 0.7. These results are shown to be in excellent agreement with the best results of other approximate methods.A new procedure for carrying out high-order coupled cluster method (CCM) [1,2,3,4,5,6,7,8] calculations via parallel processing is presented here. The CCM may be applied to systems demonstrating strong frustration and for arbitrary spatial dimension of the lattice.…”

“…A new procedure for carrying out high-order coupled cluster method (CCM) [1,2,3,4,5,6,7,8] calculations via parallel processing is presented here. The CCM may be applied to systems demonstrating strong frustration and for arbitrary spatial dimension of the lattice.…”

“…We perform a notational rotation of the "up" spins to "down" spins, as in Refs. [2,3,4,5,6,7,8] for example. We use the full symmetries of the lattice to further reduce the computational problem of finding the fundamental CCM configurations and in determining and solving the CCM equations in both cases.…”

“…However, as in Refs. [2,3,4,5,6] we may plot the sublattice magnetization against m −1 and use Padé approximants in order to carry out the extrapolations. This gives values for M in the range 0.19 to 0.20, which is again in good agreement with the best of other approximate methods, such as results from QMC [10] and ED [16] of M = 0.178 (8) and M = 0.2303, respectively.…”