We investigate an extended version of the periodic Anderson model (the so-called periodic Anderson-Hubbard model) with the aim to understand the role of interaction between conduction electrons in the formation of the heavy-fermion and mixed-valence states. Two methods are used: (i) variational calculation with the Gutzwiller wave function optimizing numerically the ground-state energy and (ii) exact diagonalization of the Hamiltonian for short chains. The
f-level occupancy and the renormalization factor of the quasiparticles are calculated as a function of the energy of the
f orbital for a wide range of the interaction parameters. The results obtained by the two methods are in reasonably good agreement for the periodic Anderson model. The agreement is maintained even when the interaction between band electrons,
Ud, is taken into account, except for the half-filled case. This discrepancy can be explained by the difference between the physics of the one- and higher-dimensional models. We find that this interaction shifts and widens the energy range of the bare
f level, where heavy-fermion behavior can be observed. For large-enough
Ud this range may lie even above the bare conduction band. The Gutzwiller method indicates a robust transition from Kondo insulator to Mott insulator in the half-filled model, while
Ud enhances the quasiparticle mass when the filling is close to half filling.
A simple variational description is given on the nature of overlapping Kondo clouds, which compensate the localized f-spins in the Kondo lattice. It is shown explicitly that the f-electrons participate in forming a “large Fermi surface”, although they are strictly localized. The resulting correlated Fermi liquid, i.e., heavy fermions, is examined with the variational Monte Carlo method and is compared with the Gutzwiller approximation. The relation to the periodic Anderson model is also discussed in this connection.