Analytical solutions of symmetric isotropic spin clusters
arXiv:2405.00214 · doi:10.3390/magnetism4030013
Abstract
Spin models like the Heisenberg Hamiltonian effectively describe the interactions of open-shell transition-metal ions on a lattice and can account for various properties of magnetic solids and molecules. Numerical methods are usually required to find exact or approximate eigenstates, but for small clusters with spatial symmetry, analytical solutions exist, and a few Heisenberg systems have been solved in closed form. This paper presents a simple, generally applicable approach to analytically solve isotropic spin clusters, based on adapting the basis to both total-spin and point-group symmetry to factor the Hamiltonian matrix into sufficiently small blocks. We demonstrate applications to small rings and polyhedra, some of which are straightforward to solve by successive spin-coupling for Heisenberg terms only; additional interactions, such as biquadratic exchange or multi-center terms necessitate symmetry adaptation.
arXiv comment23 pages, 5 figures
References in corpus (17)
- Exact spectra, spin susceptibilities and order parameter of the quantum Heisenberg antiferromagnet on the triangular lattice
- 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
- Q-dependence of the inelastic neutron scattering cross section for molecular spin clusters with high molecular symmetry
- Structure and relevant dimension of the Heisenberg model and applications to spin rings
- Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets
- Theory of high-symmetry tetramer single molecule magnets
- Combined unitary and symmetric group approach applied to low-dimensional spin systems
- 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
- Classes of integrable spin systems
- Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
- Symmetry-Induced Universal Momentum-Transfer Dependencies for Inelastic Neutron Scattering on Anisotropic Spin Clusters
- Thermodynamics of the spin square
- Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions