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 (37)

• The density-matrix renormalization group
• Stochastic series expansion method with operator-loop update
• Dynamical density-matrix renormalization-group method
• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• An SU(2) Formulation of the t-J model: Application to Underdoped Cuprates
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange
• Field induced transitions in a kagome antiferromagnet
• Independent magnon states on magnetic polytopes
• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Magnetic Properties of Undoped $C_{60}$
• The Antiferromagnetic Heisenberg Model on Clusters with Icosahedral Symmetry
• Competing Spin Phases in Geometrically Frustrated Magnetic Molecules
• 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
• Proton NMR for Measuring Quantum-Level Crossing in the Magnetic Molecular Ring Fe10
• Properties of low-lying states in some high-nuclearity Mn, Fe and V clusters: Exact studies of Heisenberg models
• Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries
• Observation of a Transient Magnetization Plateau in a Quantum Antiferromagnet on the Kagome Lattice
• Frustration effects in magnetic molecules
• The Density Matrix Renormalization Group for finite Fermi systems
• Quantum Phase Interference and Neel-Vector Tunneling in Antiferromagnetic Molecular Wheels
• Structure and relevant dimension of the Heisenberg model and applications to spin rings
• Low temperature magnetization and the excitation spectrum of antiferromagnetic Heisenberg spin rings
• Thermodynamics of a 4-site Hubbard model by analytical diagonalization
• E-band excitations in the magnetic Keplerate molecule Fe30
• Frustration effects in antiferromagnetic molecules: the cuboctahedron
• Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach
• Bounding and approximating parabolas for the spectrum of Heisenberg spin systems
• Magnetization of Mn_12 Ac in a slowly varying magnetic field: an ab initio study
• Binary trees, coproducts, and integrable systems
• Approximate eigenvalue determination of geometrically frustrated magnetic molecules
• Comment on "Bounding and approximating parabolas for the spectrum of Heisenberg spin systems" by Schmidt, Schnack and Luban
• Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann

Cited by in corpus (35)

• Magnetic Cluster Excitations
• Magnetism of the N=42 kagome lattice antiferromagnet
• Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method
• Quantum Magnetism in Minerals
• 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
• Exact diagonalization of Heisenberg $SU(N)$ chains in the fully symmetric and antisymmetric representations
• Combined use of translational and spin-rotational invariance for spin systems
• Effect of anisotropy on small magnetic clusters
• Mott physics in the half-filled Hubbard model on a family of vortex-full square lattices
• Application of the finite-temperature Lanczos method for the evaluation of magnetocaloric properties of large magnetic molecules
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• A correlator product state study of molecular magnetism in the giant Keplerate Mo72Fe30
• 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
• Advanced quantum methods for the largest magnetic molecules
• Effective theories for quantum spin clusters: Geometric phases and state selection by singularity
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• Constructions and Applications of Irreducible Representations of Spin-Space Groups
• 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
• Determination of exchange energies in the sawtooth spin ring {Mo75V20} by ESR
• The general spin triangle
• Merits of using density matrices instead of wave functions in the stationary Schrödinger equation for systems with symmetries
• Investigation of thermalization in giant-spin models by different Lindblad schemes
• 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