U-perturbation treatment of heavy fermion systems

Abstract

Heavy fermion systems are described by the periodic Anderson Model (PAM), i.e. a lattice of localized, highly correlatedf-electron states hybridized with the delocalized states of a conduction band. We treat the PAM within the second orderU perturbation theory around the non-magnetic Hartree-Fock solution (U on site Coulomb correlation between thef-electrons). This treatment has the advantage that Fermi liquid relations (Luttinger theorem) are automatically fulfilled. Thef-electron selfenergy and spectral function are calculated for different temperatures, and, for the symmetric PAM, we obtain single-particle peaks near toEf andEf+U and in addition many-particle (Kondo) resonance peaks near to the chemical potential (Ef baref-electron energy). The resonance peaks are strongly temperature dependent and vanish on a characteristic temperature scaleTK. For the symmetric PAM and a constant on-site hybridization the Fermi energy falls into a hybridization gap. A second, smaller characteristic temperature scaleTcoh (coherence temperature), on which the hybridization gap vanishes, is observed within this approach. For the non-symmetric PAM (i.e.Ef andEf+U not symmetric around the chemical potential) we obtain a similar behaviour, but the single-particle peaks are no longer at the correct positionsEf andEf+U. The proper behaviour for the symmetric PAM but less satisfactory behaviour for the non-symmetric PAM can be understood from the fact that only for the symmetric PAM the exactly solvable limit of a vanishing hybridization is reproduced within this approach.