Variational theory of valence fluctuations: Ground states and quasiparticle excitations of the Anderson lattice model.

Abstract

A variational study of ground states of the orbitally nondegenerate Anderson lattice model, using a wave function with one variational parameter per Bloch state k, has been extended to deal with essentially metallic systems having a nonintegral number of electrons per site. Quasiparticle excitations are obtained by direct appeal to Landau's original definition for interacting Fermi liquids, ${\mathrm{scrE}}_{\mathrm{q}\mathrm{p}(k}$,${\mathit{\ensuremath{\sigma}})=\mathit{\ensuremath{\delta}}\mathit{E}}_{\mathrm{total}}$/\ensuremath{\delta}n qp(k,\ensuremath{\sigma}).This approach provides a simple and explicit realization of the Luttinger picture of a periodic Fermi liquid. A close correspondence is maintained between the ``interacting'' (U=\ensuremath{\infty}) system and the corresponding ``noninteracting'' (U=0) case, i.e., ordinary band theory; the result can be described as a renormalized band or renormalized hybridization theory. The occupation-number distribution for the conduction orbitals displays a finite discontinuity at the Fermi surface. If the d-f hybridization is nonzero throughout the Brillouin zone, the quasiparticle spectrum will always exhibit a gap, although this gap becomes exponentially small (i.e., of order ${T}_{K}$) in the Kondo-lattice regime.In the ``ionic'' case with precisely two electrons per site, such a system may therefore exhibit an insulating (semiconducting) gap. The quasiparticle state density exhibits a prominent spike on each side of the spectral gap, just as in the elementary hybridization model (the U=0 case). For the metallic case, with a nonintegral number of electrons per site, the Fermi level falls within one of the two sharp density peaks. The effective mass at the Fermi surface tends to be very large; enhancements by a factor \ensuremath{\gtrsim}${10}^{2}$ are quite feasible.The foregoing variational theory has also been refined by means of a trial wave function having two variational parameters per Bloch state k. The above qualitative features are all retained, with some quantitative differences, but there are also some qualitatively new features. The most interesting of these is the appearance, within the Kondo regime, of a significant quasiparticle contribution to the f spectral weight in the vicinity of ${\ensuremath{\varepsilon}}_{f}$. The present ``one-parameter'' and ``two-parameter'' versions can be viewed as lattice generalizations of the first two approximations of the (1/${N}_{f}$)-expansion school, although our treatment of lattice aspects departs from strict 1/${N}_{f}$ methodology. The two versions have Wilson ratios \ensuremath{\equiv}1 and \ensuremath{\ne}1, respectively, consistent with (1/${N}_{f}$)-expansion studies of the single-impurity model, and a number of other features likewise show good correspondence with (1/${N}_{f}$)-expansion results.Implications are presented for the finite-temperature behaviors of several properties, especially the specific heat and electrical resistivity. Comparison with experiment then leads to some inferences about the band structures of heavy-fermion materials. A new mechanism is presented for breakup of the coherent Fermi-liquid behavior, as temperature is increased. There are two main approximations: (a) Neglect of the ``site exclusion'' problem, i.e., within cluster-expansion terms we ignore the requirement that interacting sites must all be distinct. (b) Assumption of a low density of excited quasiparticles (those excited from the ``far'' side of the hybridization gap) limits the present treatment to very low temperatures, T\ensuremath{\ll}${T}_{f}$. Electron-number conservation is treated precisely throughout.