Evaluation of the low-lying energy spectrum of magnetic Keplerate molecules using the density-matrix renormalization group technique

We apply the density-matrix renormalization-group (DMRG) technique to magnetic molecules in order to evaluate the low-lying energy spectrum. In particular, we investigate the giant Keplerate molecule $\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\}$ [A. Müller et al. Angew Chem. Int. Ed. Engl. $38,$ 3238 (1999)], where 30 ${\mathrm{Fe}}^{3+}$ ions (spins 5/2) occupy the sites of an icosidodecahedron and interact via nearest-neighbor antiferromagnetic Heisenberg exchange. The aim of our investigation is to verify the applicability and feasibility of DMRG calculations for complex magnetic molecules. To this end we first use a fictitious molecule with the same structure as $\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\}$ but with spins 1/2 as a test system. Here we investigate the accuracy of our DMRG implementation in comparison to numerically exact results [J. Schnack et al., Eur. Phys. J. B $24,$ 475 (2001)]. Then we apply the algorithm to $\{{\mathrm{Mo}}_{72}{\mathrm{Fe}}_{30}\}$ and calculate an approximation of the lowest-energy levels in the subspaces of total magnetic quantum number. The results prove the existence of a lowest rotational band, which was predicted in J. Schnack et al., Europhys. Lett. $56,$ 863 (2001).