Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory

TL;DR

This paper demonstrates that Projected Hartree-Fock (PHF) effectively approximates ground states of Heisenberg spin clusters, restoring key symmetries and providing a computationally efficient alternative to existing methods.

Contribution

It introduces a fermionic formulation of PHF for Heisenberg models and benchmarks its performance on various spin clusters, highlighting its efficiency and potential for large systems.

Findings

PHF accurately reproduces ground-state energies and correlations.

Low computational cost makes PHF suitable for large spin systems.

PHF offers a promising alternative for studying molecular spin clusters.

Abstract

We apply Projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number s. The low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of molecular spin clusters, particularly for large s and moderately large N. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.