Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach
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 disc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Condensed Matter |
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| Online Access: | https://www.mdpi.com/2410-3896/8/1/18 |
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| author | Shadan Ghassemi Tabrizi Carlos A. Jiménez-Hoyos |
| author_facet | Shadan Ghassemi Tabrizi Carlos A. Jiménez-Hoyos |
| author_sort | Shadan Ghassemi Tabrizi |
| collection | DOAJ |
| description | 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. In contrast, 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. |
| first_indexed | 2024-03-11T06:42:29Z |
| format | Article |
| id | doaj.art-1acee84fbde84651a20a9ebcaafd966d |
| institution | Directory Open Access Journal |
| issn | 2410-3896 |
| language | English |
| last_indexed | 2024-03-11T06:42:29Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Condensed Matter |
| spelling | doaj.art-1acee84fbde84651a20a9ebcaafd966d2023-11-17T10:26:53ZengMDPI AGCondensed Matter2410-38962023-02-01811810.3390/condmat8010018Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock ApproachShadan Ghassemi Tabrizi0Carlos A. Jiménez-Hoyos1Department of Chemistry, Wesleyan University, Middletown, CT 06459, USADepartment of Chemistry, Wesleyan University, Middletown, CT 06459, USARecent 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. In contrast, 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.https://www.mdpi.com/2410-3896/8/1/18molecular magnetismspin hamiltoniansquantum-chemical methodssymmetry-projection |
| spellingShingle | Shadan Ghassemi Tabrizi Carlos A. Jiménez-Hoyos Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach Condensed Matter molecular magnetism spin hamiltonians quantum-chemical methods symmetry-projection |
| title | Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach |
| title_full | Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach |
| title_fullStr | Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach |
| title_full_unstemmed | Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach |
| title_short | Ground States of Heisenberg Spin Clusters from a Cluster-Based Projected Hartree–Fock Approach |
| title_sort | ground states of heisenberg spin clusters from a cluster based projected hartree fock approach |
| topic | molecular magnetism spin hamiltonians quantum-chemical methods symmetry-projection |
| url | https://www.mdpi.com/2410-3896/8/1/18 |
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