The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model. This approach allows for a systematic evaluation of the expectation values with full Gutzwiller wave function in finite-dimensional systems. It introduces results extending in an essential manner those obtained by means of the standard Gutzwiller approximation (GA), which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss the principal paramagnetic properties and their relevance to heavy-fermion systems. We demonstrate the formation of an effective, narrow $f$ band originating from atomic $f$-electron states and subsequently interpret this behavior as a direct itineracy of $f$ electrons; it represents a combined effect of both the hybridization and the correlations induced by the Coulomb repulsive interaction. Such a feature is absent on the level of GA, which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow $f$ band rationalizes the common assumption of such dispersion of $f$ levels in the phenomenological modeling of the band structure of ${\mathrm{CeCoIn}}_5$. Moreover, it is shown that the emerging $f$-electron direct itineracy leads in a natural manner to three physically distinct regimes within a single model that are frequently discussed for $4f$- or $5f$-electron compounds as separate model situations. We identify these regimes as (i) the mixed-valence regime, (ii) Kondo/almost-Kondo insulating regime, and (iii) the Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$-state half filling, $\langle {\widehat{n}}_f\rangle \to 1$. The nonstandard features of the emerging correlated quantum liquid state are stressed.

• Received 26 May 2015

DOI:https://doi.org/10.1103/PhysRevB.92.125135