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By Murphy Ph.M.

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It becomes, thus, possible to treat the excitation processes and to describe the corresponding spectra. The above-mentioned impurity approximation was, then, considered as a starting point to investigate the finite-dimensional strongly correlated electron systems. The potential applications of the DMFT have been widely used [48, 59–61] to study the physics of these systems, in particular their phase diagrams, thermodynamic properties and their electronic characteristics. The model was used with the help of a variety of analytical and numerical techniques, such LDA, quantum Monte Carlo or numerical renormalization group.

Other functional representations like the Gutzwiller approach, the slave-boson formulation, gave equivalent results. DMFT is a non-perturbative many-body model based on the representation of the lattice onto the Anderson impurity model, recently developed and specially designed to investigate systems strongly correlated with local Coulomb interactions. Associated with the conventional LDA or GWA, it has succeeded in describing the insulating states for which the self-energy effects are crucial.

The calculations are more rapid because n(r) depends only on three coordinates, independently of the number of electrons, while the wave function of a system with N electrons depends on three coordinates for each electron. As already underlined, this model is valid for a slowly varying density as well as for high densities. 3 Electrons in Solids 19 functional formalism was very widely applied to valence electrons in solids in the ground state. Physical properties associated with crystalline stability of the ground state were calculated, such as cohesive energy, compressibility and elastic constants.

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