Numerically exact and approximate determination of energy eigenvalues for antiferromagnetic molecules using irreducible tensor operators and general point-group symmetries

Abstract

Numerical exact diagonalization is the ultimate method of choice in order to discuss static, dynamic, and thermodynamic properties of quantum systems. In this article we consider Heisenberg spin-systems and extend the range of applicability of the exact diagonalization method by showing how the irreducible tensor operator technique can be combined with an unrestricted use of general point-group symmetries. We also present ideas how to use spin-rotational and point-group symmetries in order to obtain approximate spectra.

10 pages, 11 figures, submitted to Phys. Rev. B

References in corpus (14)

• The density-matrix renormalization group
• Stochastic series expansion method with operator-loop update
• Rotational modes in molecular magnets with antiferromagnetic Heisenberg exchange
• Enhanced magnetocaloric effect in frustrated magnetic molecules with icosahedral symmetry
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Properties of low-lying states in some high-nuclearity Mn, Fe and V clusters: Exact studies of Heisenberg models
• Quantum rotational band model for the Heisenberg molecular magnet Mo72Fe30
• Frustration effects in magnetic molecules
• 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
• E-band excitations in the magnetic Keplerate molecule Fe30
• Correlations for the S=1/2 Antiferromagnet on a Truncated Tetrahedron
• Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach
• Magnetization of Mn_12 Ac in a slowly varying magnetic field: an ab initio study

Cited by in corpus (29)

• Effects of frustration on magnetic molecules: a survey from Olivier Kahn till today
• Magnetic Cluster Excitations
• Exact diagonalization: the Bose-Hubbard model as an example
• Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method
• High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields
• Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
• Heat capacity uncovers physics of a frustrated spin tube
• Enhanced magnetocaloric effect in a proximity of magnetization steps and jumps of spin-1/2 XXZ Heisenberg regular polyhedra
• Magnetic Exchange Interactions in the Molecular Nanomagnet Mn${}_{12}$
• The Schottky-type specific heat as an indicator of relative degeneracy between ground and first-excited states: the case study of regular Ising polyhedra
• Advanced Finite-Temperature Lanczos Method for anisotropic spin systems
• 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
• Projection operator approach to spin diffusion in the anisotropic Heisenberg chain at high temperatures
• Effect of anisotropy on small magnetic clusters
• Application of the finite-temperature Lanczos method for the evaluation of magnetocaloric properties of large magnetic molecules
• A correlator product state study of molecular magnetism in the giant Keplerate Mo72Fe30
• Influence of intermolecular interactions on magnetic observables
• Exact diagonalization of $\mathrm{SU}(N)$ Heisenberg and AKLT chains using the full $\mathrm{SU}(N)$ symmetry
• Advanced quantum methods for the largest magnetic molecules
• Thermodynamic observables of Mn12-acetate calculated for the full spin-Hamiltonian
• Binary trees, coproducts, and integrable systems
• Spin-1/2 $XXZ$ Heisenberg cupolae: magnetization process and related enhanced magnetocaloric effect
• 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
• Projective spin adaptation for the exact diagonalization of isotropic spin clusters
• Magnetization curves of deposited finite spin chains
• 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