DMFT equations the relation between the two orbitals in the lattice problem. The fluctuations at the $f$-orbital are in fact composed of two contributions: (a) the on-site quantum fluctuations and (b) indirect delocalization through conduction band proportional to squared hybridization amplitude.

The DMFT solution requires therefore to compute the impurity Green’s function where the symbol $\bra \, \ket_{\rm S_{\rm eff}}$ indicates the average with respect to the effective action (\[Seff\]). From the knowledge of the impurity Green’s function it is straightforward to determine the self-energy: $$\Sigma(\iome)_\s=\Sigma^{\rm imp}_\s(\iome)=\GG_{0\s}^{-1}(\iome)-{G^{\rm imp}_\s}^{-1}
(\iome)$$ and finally to evaluate the local Green’s function: $$G_{p\s}(\iome)=\int
d\varepsilon\frac{D(\varepsilon)}{\iome+\mu-\ep0-\Sigma_{p\s}(\iome)-\varepsilon}$$ Then a new Weiss field can be computed and the procedure can be iterated until convergence is achieved.

The solution of the effective impurity problem, , is the bottleneck of the DMFT algorithm. In this work we use a combination of numerical techniques:[@rmp] Hirsch-Fye Quantum Monte Carlo (QMC) [@kotliarRMP; @dosSantos03] and Exact Diagonalization (ED) methods, both in the full diagonalization and Lanczos algorithm implementations, at zero[@dagottoRMP] and finite temperature.[@lucaED] The ED method is based on a discretization of the effective bath on an adaptive energy grid. In this paper we present full ED calculations in which the bath is described by 