this model since its early stages.[@jarrell; @marcelo_PAM]

Within DMFT a lattice model is mapped onto an effective single-impurity problem, fixed by a self-consistency condition which enforces the equivalence between the two models as far as the local physics is concerned.[@phytoday; @rmp] The scheme is equivalent to a local approximation on the self-energy, which becomes momentum independent.

The DMFT equations can be obtained using a quantum cavity method. The effective action of the single $f$-orbital impurity problem is obtained integrating out all lattice degrees of freedom except for a chosen site (labeled conventionally as site $i=0$) and keeping only the first term in the expansion[@metzvol; @rmp] in terms of many-particle Green’s functions:

The action $S_\mathrm{eff}$ is expressed in terms of the local [*Weiss Field*]{} $\GG_{0\s}^{-1}(\iome)$, describing the quantum fluctuations at the correlated $f$-orbital. The Weiss field satisfies a self-consistence equation which depends on the lattice under consideration. In this work we consider a Bethe lattice with semi-elliptical density of states of half-bandwidth $D$ (fixing the energy unit of the problem), $D(\varepsilon) =
\frac{2}{\pi D^2}\sqrt{D^2-\varepsilon^2}$. In this case the self-consistency is particularly simple and reads: where $G_{p\s}$ is the conduction electron local Green’s function. The functional form of $\GG_{0\s}^{-1}$ mirrors in the 