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

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.