Hollender, Lucas (2012) From Periodic to Dilute Anderson Models. PhD thesis, Universität zu Köln.
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Actinide- and Lanthanide based compounds are often considered as heavy Fermion (HF) systems. The essential ingredient for these systems is a localized d- or f-shell electron per lattice site which hybridizes with a non-interacting conduction band of p- or d-shell electrons. For temperatures below the so called coherence temperature Tc, the localized electrons stop to act like mag- netic scatterers known from the Kondo effect. There the conduction band electrons screen the local magnetic moments coherently. As a main effect the conduction electrons build a Fermi liquid (FL) of quasiparticles with strongly enhanced masses which exceed 10-1000 times the mass of the original electrons. These enhancements can be seen experimentally in an increased heat capacity coefficient and Pauli susceptibility. In this work we employ the periodic Anderson model (PAM) to describe the paramagnetic phase of the heavy Fermion compounds. To solve the compli- cated many body problem the dynamical mean-field theory is adopted with the numerical renormalization group technique as impurity solver. We find that for low conduction band fillings Tc decreases drastically, which is in accordance with the exhaustion effect predicted by Nozières . Additionally we find, that the form of the free conduction band density of states is decisive to obtain a FL or a Mott insulating (MI) phase for strongly depleted conduction band fillings. Furthermore we investigate the PAM on a bipartite lattice, the coherence temperatures for each sublattice and especially the case of vanishing hybridiza- tion for one sublattice. In the latter case the system resembles a conduction band with only half the localized moment sites coupled to it. Our results show that it depends strongly on the chosen parameters if there is only one scale for the whole lattice or two distinct scales for each sublattice. Especially decoupling one sublattice leads to two separated scales. In the last part the attention is focused on the two-impurity Anderson model and its solution via the DMFT method. We investigate the Anderson model and compare results to direct NRG calculations. Importantly, the two-impurity DMFT method can be easier extended to multi-impurity systems than the NRG on its own. This might lead to a method to efficiently examine multi- impurity systems.
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