Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters

Shadan Ghassemi Tabrizi; Thomas D. Kühne

doi:10.3390/magnetism5010008

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arXiv · 2501.01160

Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters

Shadan Ghassemi Tabrizi·Thomas D. Kühne

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Abstract

While either spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin S and the irreducible representation of the point-group is limited by the complexity of transformations between different coupling-schemes that are related by 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 that we illustrate with applications to Heisenberg spin-rings and polyhedra, including systems that are computationally inaccessible with conventional coupling-techniques.

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Shadan Ghassemi Tabrizi, Thomas D. Kühne. 2025-01-02. Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters. https://doi.org/10.3390/magnetism5010008

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