aforementioned tendency to form local Zhang-Rice-singlets, driven by the hole-doping, and the incoherent nature of the scatterer provided by the $f$-electron local moments, driven by Mott physics. At large doping the increased number of available holes of $p$-type helps the formation of a many-body coherent state without breaking the local binding with $f$-moment. This arguments will be substantiated by the calculations that we report in the following sections.

![(Color online) Scaling of the inverse life-time $\tau^{-1}$ as a function of $T^2$ in the small temperature limit. Data are from Lanczos ED calculations. Lines are guide to the eye. []{data-label="fig2.6"}](fig7.eps){width="45.00000%"}

The coherence temperature {#sec3.1}
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The analysis of the self-energy and of the carriers lifetime clearly shows the existence of a small doping-dependent energy scale associated with the appearance of an incoherent metal. We expect this scale to influence also other observables, like the local spin susceptibility: $$\chi_\mathrm{loc}(T)=\intbeta\bra S_{zf}(\t)\cdot S_{zf}(0)\ket  d\t$$

This quantity describes the response to a [*local*]{} magnetic field and easily discriminates between a Fermi-liquid, in which the zero-temperature limit is a constant (Pauli susceptibility), and a paramagnetic Mott insulator in which it diverges like $1/T$ (Curie behavior).

The results are reported in . In the Mott insulating state 