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We apply Projected Hartree-Fock theory (PHF) for approximating ground statesof Heisenberg spin clusters. Spin-rotational, point-group andcomplex-conjugation symmetry are variationally restored from a broken-symmetrymean-field reference, where the latter corresponds to a product of local spinstates. A fermionic formulation of the Heisenberg model furnishes a conceptualconnection to PHF applications in quantum chemistry and detailed equations fora self-consistent field optimization of the reference state are provided.Different PHF variants are benchmarked for ground-state energies and spin-paircorrelation functions of antiferromagnetic spin rings and three differentpolyhedra, with various values of the local spin-quantum number s. The lowcomputational cost and the compact wave-function representation make PHF apromising complement to existing approaches for ground states of molecular spinclusters, particularly for large s and moderately large N. The present work mayalso motivate future explorations of more accurate post-PHF methods forHeisenberg spin clusters.

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