Ground states of Heisenberg spin clusters from a cluster-based projected Hartree-Fock approach

TL;DR

This paper extends projected Hartree-Fock theory to a cluster-based approach for approximating ground states of Heisenberg spin clusters, improving accuracy by including intracluster correlations and restoring symmetries.

Contribution

It introduces a cluster-based projected Hartree-Fock (cPHF) method that enhances ground state approximations of spin clusters by grouping sites into clusters and restoring symmetries.

Findings

cPHF improves over ordinary PHF in accuracy

cPHF yields states with correct symmetry quantum numbers

Cluster grouping can preserve full spatial symmetry in certain arrangements

Abstract

Recent work on approximating ground states of Heisenberg spin clusters by projected Hartree-Fock theory (PHF) is extended to a cluster-based ansatz (cPHF). Whereas PHF variationally optimizes a site-spin product state for the restoration of spin- and point-group symmetry, cPHF groups sites into discrete clusters and uses a cluster-product state as the broken-symmetry reference. Intracluster correlation is thus already included at the mean-field level and intercluster correlation is introduced through symmetry projection. Variants of cPHF differing in the broken and restored symmetries are evaluated for ground states and singlet-triplet gaps of antiferromagnetic spin rings for various cluster sizes, where cPHF in general affords a significant improvement over ordinary PHF, although the division into clusters lowers the cyclical symmetry. On the other hand, certain two- or three-dimensional spin arrangements permit cluster groupings compatible with the full spatial symmetry. We accordingly demonstrate that cPHF yields approximate ground states with correct spin and point-group quantum numbers for honeycomb lattice fragments and symmetric polyhedra.