Periodic Anderson model

THE PERIODIC ANDERSON MODEL IN THE GENERATING FUNCTIONAL APPROACH... 

Abstract The periodic Anderson model at arbitrary values of the on-site Coulomb... 

Likewise the Hubbard model the periodic Anderson model (PAM) is a basic model in the theory of strongly correlated electron systems. It is destined for the description of the transition metals, lanthanides, actinides and their compositions including the heavy-fermion compounds. The model consists of two groups of electrons itinerant and localized ones (s and d electrons), the hybridization between them is admitted. The model is described by the following parameters the width of the s-electron band W, the energy of the atomic level e, the on-site Coulomb repulsion U of d-electrons with opposite spins, the parameter V of the... 

The periodic Anderson model in the generating functional approach... 

We applied the generating functional approach to the periodic Anderson model. Calculation of the electron GFs gdd, 9ds, 9sd and gss reduces to calculation of only the d-electron GF. For this, an exact matrix equation was derived with the variational derivatives. Iterations with respect to the effective matrix element Aij(to) allow to construct a perturbation theory near the atomic limit. Along with the self-energy, the terminal part of the GF Q is very important. The first order correction for it describes the interaction of d-electrons with spin fluctuations. In the paramagnetic phase this term contains a logarithmic singularity near the Fermi-level and thus produces a Kondo-like resonance peak in the d-electron density of states. The spin susceptibility of d-electrons... 

From a technical point of view, calculations for a lattice-periodic Anderson model in the Fermi-hquid phase account for the coherent action of many 4f-shells as scattering centers in the following way (Grewe 1987, Grewe et al. 1988) ... 

We illustrate the formation of coherence in the one-particle DOS again in fig. 9a for the band states. The calculation, like the ones before, is based on the lattice version of the NCA technique (LNCA), which has been outlined above. It leads to temperatiure-dependent spectra for both kinds of electrons, cf. also fig. 4b. The band states do not reflect the enhancement of the DOS, which is due to the local states, but they react simultaneously by the formation of a gap of the same size to the increase of local scattering at all lattice sites with decreasing temperature. Clearly the change in DOS near Ep reflects the characteristic temperature T, which can roughly be determined from the size of the gap. For comparison, a calculation for the IV regime of the periodic Anderson model is in addition shown in fig. 9b. The spectrum is less temperature dependent, due to the... 

In model calculations using, e.g., the LNCA technique in connection with the periodic Anderson model, T is most easily extracted from the width or the position of the ASR in the local one-particle spectral density (Kuramoto and Muller-Hartmann 1985, Bickers et al. 1987, Pruschke and Grewe 1989). It coincides with the Kondo temperature for an f-impurity and acquires some modest corrections for the lattice case (Grewe et al. 1988). The aforementioned characterizations of T are, to a large degree, substantiated by such calculations, too. Collective effects in heavy-fermion systems pose a much harder problem for solid state theory, which has met only partial success imtil today. 

In the periodic Anderson model state of the electrons of the crystal containing impurities in the 7i-electron approximation and the nearest neighbor approximation is described by the effective Hamiltonian, having the following standard form [5] ... 

The basis for our understanding of VF and HF compounds is the periodic Anderson model... 

Fig. 17. Sketch of the dispersion relation e(k) for quasi-particle bands, as derived from the periodic Anderson model in a mean-field approximation (Millis and Lee...

Near the Ce or Yb end of the R series, the 4f level thus approaches the Fermi level in energy and the 4f electrons hybridize more strongly with the conduction electrons with the kinetic energy E. This f-hybridized coupling constant is denoted by V. A theoretical treatment for such a system is called the periodic Anderson model (Anderson 1961). The parameters E, V, Ef and U predominantly control the dynamics of tiie system. These values depend actually on the crystal structure. The relation between flie magnetic ordering temperature and the distance between the Ce (or U) atoms is known as a Hill plot (Hill 1970). 

Ce3Bi4Pt3 [245]) charge gap development in the Kondo insulators involves a redistribution of spectral weight from low to high frequencies, and influences electronic states over an energy scale that is much higher than the characteristic temperature at which gap development occurs. In the case of the Kondo insulators, the dramatic spectral weight redistribution is nicely accounted for in calculations of the periodic Anderson model [72]. 

Heavy fermion materials are usually modeled by the single impurity Anderson model or the periodic Anderson model depending on the concentration of the correlated f orbitals. Although at high temperatures the SIM captures the same physics as the lattice model, it caimot account for the electronic coherence at low temperatures. The periodic Anderson model (PAM) is believed to describe the strong correlation of f electrons as well as their... 

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