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

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.

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Cited by in corpus (5)

• Symmetry-projected cluster mean-field theory applied to spin systems
• Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach
• Projective spin adaptation for the exact diagonalization of isotropic spin clusters
• Analytical solutions of symmetric isotropic spin clusters
• Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions