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The recently proposed diagrammatic expansion (DE) technique for the fullGutzwiller wave function (GWF) is applied to the Anderson lattice model (ALM).This approach allows for a systematic evaluation of the expectation values withGWF in the finite dimensional systems. It introduces results extending in anessential manner those obtained by means of standard Gutzwiller Approximation(GA) scheme which is variationally exact only in infinite dimensions. Withinthe DE-GWF approach we discuss principal paramagnetic properties of ALM andtheir relevance to heavy fermion systems. We demonstrate the formation of aneffective, narrow $f$-band originating from atomic $f$-electron states andsubsequently interpret this behavior as a mutual intersite $f$-electroncoherence; a combined effect of both the hybridization and the Coulombrepulsion. Such feature is absent on the level of GA which is equivalent to thezeroth order of our expansion. Formation of the hybridization- andelectron-concentration-dependent narrow effective $f$-band rationalizes commonassumption of such dispersion of $f$ levels in the phenomenological modeling ofthe band structure of CeCoIn$_5$. Moreover, we show that the emerging$f$-electron coherence leads in a natural manner to three physically distinctregimes within a single model, that are frequently discussed for 4$f$- or 5$f$-electron compounds as separate model situations. We identify these regimes as:(i) mixed-valence regime, (ii) Kondo-insulator border regime, and (iii)Kondo-lattice limit when the $f$-electron occupancy is very close to the $f$electrons half-filling, $\langle\hat n_{f}\rangle\rightarrow1$. The non-Landaufeatures of emerging correlated quantum liquid state are stressed.

Gutzwiller Wave-Function Solution for Anderson Lattice Model: Emerging Universal Regimes of Heavy Quasiparticle States