The low-temperature elementary spin excitations in the AFM molecular wheel Fe 18 were studied experimentally by inelastic neutron scattering and theoretically by modern numerical methods, such as dynamical density matrix renormalization group or quantum Monte Carlo techniques, and analytical spin-wave theory calculations. Fe 18 involves eighteen spin-5/2 Fe III ions with a Hilbert space dimension of ∼10 14 , constituting a physical system that is situated in a region between microscopic and macroscopic. The combined experimental and theoretical approach allowed us to characterize and discuss the magnetic properties of Fe 18 in great detail. It is demonstrated that physical concepts such as the rotational-band or L and E-band concepts developed for smaller rings are still applicable. In particular, the higher-lying low-temperature elementary spin excitations in Fe 18 or AFM wheels, in general, are of discrete antiferromagnetic spin-wave character.

Abstract. For the time being isotropic three-body exchange interactions are scarcely explored and mostly used as a tool for constructing various exactly solvable one-dimensional models, although, generally speaking, such competing terms in generic Heisenberg spin systems can be expected to support specific quantum effects and phases. The Heisenberg chain constructed from alternating S = 1 and σ = 1 2 site spins defines a realistic prototype model admitting extra three-body exchange terms. Based on numerical density-matrix renormalization group (DMRG) and exact diagonalization (ED) calculations, we demonstrate that the additional isotropic three-body terms stabilize a variety of partially-polarized states as well as two specific non-magnetic states including a critical spin-liquid phase controlled by two Gaussinal conformal theories as well as a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. Most of the established effects are related to some specific features of the three-body interaction such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest-neighbor clustering of the spins. It may be expected that most of the predicted effects of the isotropic three-body interaction persist in higher space dimensions.PACS. 75.10.Jm Quantized spin models -75.40.Mg Numerical simulation studies -75.45.+j Macroscopic quantum phenomena in magnetic systems

a b s t r a c tWe present up to date investigations of the antiferromagnetic Heisenberg icosidodecahedron by means of the density matrix renormalization group method. We compare our results with modern correlator product state as well as Lanczos calculations.

We discuss modern numerical methods for quantum spin systems and their application to magnetic molecules.