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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 interactions between magnetic moments are mediated by the conduction electrons through a mechanism understood in terms of 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 other quantum phenomena: the Kondo effect. This competition is quite subtle and non-trivial, and can only be studied by numerical means. We explore these phenomena on different lattice geometries in 1,2 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 departure from conventional RKKY theory and important differences that can be attributed to dimensionality and geometry. In particular, for the square and cubic lattices at half filling, Kondo physics dominates even at short distances, while the ferromagnetic RKKY state is energetically unfavorable, translating into a finite range for the RKKY interaction. In the case of larger spin S=1, RKKY correlations can coexist with (partial) screening.

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Adrian Feiguin, Northeastern University
Konferenzraum Theorie, Altbau
Contact: Simon Trebst