High-Order Coupled Cluster Calculations Via Parallel Processing: An Illustration For CaV$_4$O$_9$

TL;DR

This paper introduces a parallelized high-order coupled cluster method enabling more accurate quantum many-body calculations, demonstrated on a frustrated magnetic material, with results aligning well with existing methods.

Contribution

The paper presents a novel parallelization approach for high-order CCM calculations, significantly extending computational capabilities for complex quantum spin systems.

Findings

Extended CCM calculations by an order of magnitude.

Achieved accurate ground-state energy and magnetization for CaV$_4$O$_9$.

Predicted absence of Néel order in certain parameter ranges.

Abstract

The coupled cluster method (CCM) is a method of quantum many-body theory that may provide accurate results for the ground-state properties of lattice quantum spin systems even in the presence of strong frustration and for lattices of arbitrary spatial dimensionality. Here we present a significant extension of the method by introducing a new approach that allows an efficient parallelization of computer codes that carry out ``high-order'' CCM calculations. We find that we are able to extend such CCM calculations by an order of magnitude higher than ever before utilized in a high-order CCM calculation for an antiferromagnet. Furthermore, we use only a relatively modest number of processors, namely, eight. Such very high-order CCM calculations are possible {\it only} by using such a parallelized approach. An illustration of the new approach is presented for the ground-state properties of a highly frustrated two-dimensional magnetic material, CaV$_4$O$_9$. Our best results for the ground-state energy and sublattice magnetization for the pure nearest-neighbor model are given by $E_g/N=-0.5534$ and $M=0.19$, respectively, and we predict that there is no N\'eel ordering in the region $0.2 \le J_2/J_1 \le 0.7$. These results are shown to be in excellent agreement with the best results of other approximate methods.