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. Thermodynamic observables such as the magnetization are then easily evaluated. In addition it provides a spectroscopic labeling by irreducible representations that can be related to selection rules which can be helpful when interpreting transitions induced by electron paramagnetic resonance, nuclear magnetic resonance or inelastic neutron scattering. It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.

Keywords:

• Heisenberg model
• numerically exact energy spectrum
• irreducible tensor operators
• approximate diagonalization

Acknowledgements

We thank Dante Gatteschi, Boris Tsukerblat, Martin Höck, and Jörg Ummethum for carefully reading the manuscript. This work was supported by the German Science Foundation (DFG) through the research group 945 and a Ph.D. program of the State of Lower Saxony at Osnabrück University. Computing time at the Leibniz Computing Center in Garching is also gratefully acknowledged. Last but not least we would like to thank the State of North Rhine-Westphalia and the DFG for financing our local SMP supercomputer as well as the companies BULL and ScaleMP for constant support.