Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters
While either a spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin <i>S</i> and the irreducible representation <inline-formula><math xmlns="http://www.w3.org/1998...
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2025-03-01
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| author | Shadan Ghassemi Tabrizi Thomas D. Kühne |
| author_facet | Shadan Ghassemi Tabrizi Thomas D. Kühne |
| author_sort | Shadan Ghassemi Tabrizi |
| collection | DOAJ |
| description | While either a spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin <i>S</i> and the irreducible representation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula> of the point group is limited by the complexity of the transformations between different coupling schemes that are related in terms of their site permutations. To overcome these challenges, we apply projection operators directly to uncoupled basis states, enabling the simultaneous treatment of spin and point-group symmetry without the need for recoupling transformations. This provides a simple and efficient approach for the exact diagonalization of isotropic spin models, which we illustrate, with applications in Heisenberg spin rings and polyhedra, including systems that are computationally inaccessible with conventional coupling techniques. |
| format | Article |
| id | doaj-art-a77eeeee1f6541f7ba02bc2a6676e1f8 |
| institution | OA Journals |
| issn | 2673-8724 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Magnetism |
| spelling | doaj-art-a77eeeee1f6541f7ba02bc2a6676e1f82025-08-20T01:49:00ZengMDPI AGMagnetism2673-87242025-03-0151810.3390/magnetism5010008Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin ClustersShadan Ghassemi Tabrizi0Thomas D. Kühne1Center for Advanced Systems Understanding (CASUS), Am Untermarkt 20, 02826 Görlitz, GermanyCenter for Advanced Systems Understanding (CASUS), Am Untermarkt 20, 02826 Görlitz, GermanyWhile either a spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin <i>S</i> and the irreducible representation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula> of the point group is limited by the complexity of the transformations between different coupling schemes that are related in terms of their site permutations. To overcome these challenges, we apply projection operators directly to uncoupled basis states, enabling the simultaneous treatment of spin and point-group symmetry without the need for recoupling transformations. This provides a simple and efficient approach for the exact diagonalization of isotropic spin models, which we illustrate, with applications in Heisenberg spin rings and polyhedra, including systems that are computationally inaccessible with conventional coupling techniques.https://www.mdpi.com/2673-8724/5/1/8spin Hamiltoniansexact diagonalizationsymmetrymolecular magnetism |
| spellingShingle | Shadan Ghassemi Tabrizi Thomas D. Kühne Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters Magnetism spin Hamiltonians exact diagonalization symmetry molecular magnetism |
| title | Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters |
| title_full | Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters |
| title_fullStr | Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters |
| title_full_unstemmed | Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters |
| title_short | Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters |
| title_sort | simultaneous spin and point group adaptation in exact diagonalization of spin clusters |
| topic | spin Hamiltonians exact diagonalization symmetry molecular magnetism |
| url | https://www.mdpi.com/2673-8724/5/1/8 |
| work_keys_str_mv | AT shadanghassemitabrizi simultaneousspinandpointgroupadaptationinexactdiagonalizationofspinclusters AT thomasdkuhne simultaneousspinandpointgroupadaptationinexactdiagonalizationofspinclusters |