Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

Abstract

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.

29 pages, many figures

References in corpus (7)

• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Metamagnetic phase transition of the antiferromagnetic Heisenberg icosahedron
• Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries
• E-band excitations in the magnetic Keplerate molecule Fe30
• Frustration effects in antiferromagnetic molecules: the cuboctahedron

Cited by in corpus (21)

• Accuracy of the finite-temperature Lanczos method compared to simple typicality-based estimates
• Discrete antiferromagnetic spin-wave excitations in the giant ferric wheel Fe18
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• 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
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Eigenstate thermalization hypothesis in two-dimensional XXZ model with or without SU(2) symmetry
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• Observation of phase synchronization and alignment during free induction decay of quantum spins with Heisenberg interactions
• Symmetry-Induced Universal Momentum-Transfer Dependencies for Inelastic Neutron Scattering on Anisotropic Spin Clusters
• Simultaneous Spin and Point-Group Adaptation in Exact Diagonalization of Spin Clusters
• Analytical solutions of symmetric isotropic spin clusters
• Projective spin adaptation for the exact diagonalization of isotropic spin clusters
• Thermal DMRG for highly frustrated quantum spin chains: a user perspective
• Quantum Entanglement Generation in the Heterometallic Ni${}_4^{\text{2+}}$Gd${}_4^{\text{3+}}$ Complexes
• Faster randomized partial trace estimation