Anderson Hamiltonian excitation energies

Having established the relationship between the parameters entering the Anderson Hamiltonian and high-energy excitations it is very instructive to illustrate the physical message delivered by this Hamiltonian within the simplest model which... 

We shall see in section 6.2 that this extremely simple model provides a qualitatively correct picture of high-energy spectra of light lanthanide solids. Similar approaches to excitation spectra of lanthanides have been introduced for clusters (Fujimori 1983, Fujimori and Weaver 1985) and have been considered for solids (Kotani et al. 1985). It must be emphazised, however, that the use of a few molecular orbitals in these simplified models of the Anderson impurity Hamiltonian leads to spectra where the excitations appear necessarily as discrete lines. This approach to a solid is missing irremediably the continuum aspects of the band states interacting with the f state. For example, one unrealistic consequence of a cluster model is the fact that the lowest excitation energies are typically of the order of the hybridization energy for both, metals and insulators. This implies zero specific heat and too small susceptibilities for metallic systems (Fujimori et al. 1984). Nevertheless, such models... 

The essential point we wish to convey is that the Anderson Hamiltonian with one set of parameters ( f, U, and is capable of explaining the high energy ( 1 eV) excitation properties measured by XPS and BIS as well as the low energy ( 0.01eV) equilibrium properties in dilute and concentrated Ce and Yb materials. 

The ZSA phase diagram and its variants provide a satisfactory description of the overall electronic structure of stoichiometric and ordered transition-metal compounds. Within the above description, the electronic properties of transition-metal oxides are primarily determined by the values of A, and t. There have been several electron spectroscopic (photoemission) investigations in order to estimate the interaction strengths. Valence-band as well as core-level spectra have been analysed for a large number of transition-metal and rare-earth compounds. Calculations of the spectra have been performed at different levels of complexity, but generally within an Anderson impurity Hamiltonian. In the case of metallic systems, the situation is complicated by the presence of a continuum of low-energy electron-hole excitations across the Fermi level. These play an important role in the case of the rare earths and their intermetallics. This effect is particularly important for the valence-band spectra. 

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