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

TL;DR

This paper introduces a novel method for exact diagonalization of spin models that simultaneously incorporates spin and point-group symmetries using projection operators, simplifying calculations for complex systems.

Contribution

The authors develop a direct projection-operator approach that avoids complex recoupling transformations, enabling efficient symmetry treatment in spin Hamiltonian diagonalization.

Findings

Applicable to Heisenberg spin rings and polyhedra

Handles systems inaccessible to traditional methods

Improves computational efficiency and simplicity

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.