Electron-Phonon Interactions in d-, f- electron systems. The influence of lattice vibrations on the electronic properties of condensed matter systems at different scales is well established, such as for example in superconductivity, electronic/thermal transport, Jahn-Teller molecular transitions, surface adsorption, etc. Phonons are known to affect the properties of many Heavy-Fermion and Mixed-Valence systems, and more generally isolated and dense magnetic impurities in metallic hosts. Also, phonon effects are relevant to the behavior of spin excitations in spin-tunnelling junctions, and to the magnetic moment dissipation mechanisms in quantum dots. The effect of phonons on localized magnetic impurities has received so far limited theoretical attention: the available investigations primarily characterize phonons as a mechanism for (magnetic) moment reduction. At this stage, there is scope for model calculations of small systems, aimed to gain more insight in this and similar issues. Preliminary exact diagonalization results show that phonons can also enhance single impurity magnetism, depending on the type and strength of phonon coupling, the impurity level position and the electron density. Such behavior is expected to manifest also in the dense impurity regime. Figure 3 Caption: Exact diagonalization results in the large U, V, U/V limit for a single impurity Anderson Model cluster with local electron-phonon interactions (Anderson-Holstein model, schematically shown at the bottom left). The impurity level is close to the highest occupied band level. The dependence of the ground state occupation number and spin correlation functions <(Szf)2>, <(Szc)2>, |<(Szf Szc>| on the electron-phonon coupling is shown.
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