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

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.

21 pages, 12 figures

References in corpus (17)

• Triaxial magnetic anisotropy in the two-dimensional ferromagnetic semiconductor CrSBr
• Magnetism of the N=42 kagome lattice antiferromagnet
• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Properties of low-lying states in some high-nuclearity Mn, Fe and V clusters: Exact studies of Heisenberg models
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries
• Q-dependence of the inelastic neutron scattering cross section for molecular spin clusters with high molecular symmetry
• Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets
• Theory of high-symmetry tetramer single molecule magnets
• Communication: Curing basis set overcompleteness with pivoted Cholesky decompositions
• Antiferromagnetic Heisenberg Model on the Icosahedron: Influence of Connectivity and the Transition from the Classical to the Quantum Limit
• Combined use of translational and spin-rotational invariance for spin systems
• Fully Symmetrized VB Based Technique for Solving Exchange Hamiltonians of Molecular Magnets
• Advanced quantum methods for the largest magnetic molecules
• Full Spin and Spatial Symmetry Adapted Technique for Correlated Electronic Hamiltonians: Application to an Icosahedral Cluster
• Analytical solutions of symmetric isotropic spin clusters
• Projective spin adaptation for the exact diagonalization of isotropic spin clusters