From mesoscopic magnet to quantum wire. The Bethe Ansatz application

Molecular nanomagnets are representatives of quantum systems in which significant magnetic size effects are observed. In most cases they are formed of a few or a dozen or so magnetic ions arranged into a regular ring (e.g. Fe8). Such small chains can be treated as quantum wires. In literature magnetic properties of these systems were studied experimentally and these results confirm fully their extraordinary quantum features. By far results were interpreted basing on solutions obtained numerically. In present paper we give the exact solutions of the system, obtained basing on the Bethe theory. The application of this theory for such small systems is quite complicated. We develop mathematical method for inspection of the solutions evolution starting from macroscopic via mesoscopic till nanoscopic size of the Heisenberg chain. Furthermore, we study the properties of the energy band structures (as noncrossing, rarefied effect, etc.) and their changes as a function of magnetic quantum dots size.