Hosted by: Alexei Tsvelik

In the past decade we have witnessed enormous progress in experiments that consist of placing magnetic atoms at predetermined positions on substrates and building magnetic nanostructures one atom at a time. The effective interaction between spins is mediated by the conduction electrons in the substrate. In order to understand these interactions, we rely on a theory developed decades ago by Ruderman, Kittel, Kasuya, and Yosida, dubbed "RKKY theory", which applies when the spins are classical. The quantum nature of the electronic spin introduces another degree of complexity and competition with another quantum phenomenon: the Kondo effect. This competition is quite subtle and non-trivial, and can only be studied by numerical means. We investigate this mechanism on different lattice geometries in 2 and 3 dimensions by introducing an exact mapping onto an effective one-dimensional problem that we can solve with the density matrix renormalization group method (DMRG). We show a clear and departure from the conventional RKKY theory, and important differences that can be attributed to the dimensionality and geometry. We have found that there is a critical distance at which the Kondo effect dominates, translating into a finite range for the RKKY interaction. In particular, for dimension d>1, Kondo physics dominates even at short distances, while the ferromagnetic RKKY state is energetically unfavorable. Remarkably, in the case of impurities with higher spin S=1, both effects can co-exist: while the impurities are partially screened by the conduction electrons, an effective dangling spin S=1/2 is responsible for the entanglement between impurities.