The power of typicality applied to magnetic molecules and low-dimensional quantum spin systems

Molecular or low-dimensional quantum spin systems often prevent an exact calculation of their magnetic properties due to a prohibitively large size of the related Hilbert spaces. Typicality-based approaches such as the finite-temperature Lanczos method allow to investigate rather large
systems with unprecedented accuracy. This way quantum critical as well as magnetocaloric properties of large cyclic clusters could be elucidated. For the kagome lattice antiferromagnet it became possible to model a lattice of size N=42 (!) quasi exactly. This enabled us to study in particular that the low-lying density of singlet states moves up in energy contrary to common believe. In addition, we could demonstrate for lattices up to 72 sites that magnon crystallization occurs slightly below the saturation field, an effect driven by the existance of flat energy bands.
[1] A. Baniodeh et al., High spin cycles: topping the spin record for a single molecule verging on quantum criticality, npj Quantum Materials 3,10 (2018)
[2] J. Schnack, J. Schulenburg, J. Richter, Magnetism of the N=42 kagome lattice antiferromagnet, Phys. Rev. B 98, 094423 (2018)
[3] J. Schnack, J. Schulenburg, A. Honecker, J. Richter, Magnon crystallization in the kagome lattice antiferromagnet, arXiv:1910.10448