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

TL;DR

This paper reviews numerical methods that leverage real- and spin-space symmetries to efficiently calculate the energy spectra of small magnetic molecules, aiding interpretation of spectroscopic data.

Contribution

It introduces a detailed approach to diagonalize the Heisenberg Hamiltonian using combined symmetries, enabling analysis of larger spin systems and spectroscopic labeling.

Findings

Enhanced ability to treat larger spin systems

Block-diagonalization of Hamiltonian using symmetries

Spectroscopic labels aid in interpreting experimental data

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.