doping-driven metalization appears as the process of delocalizing a multi-band “Zhang-Rice-like" singlet state, formed by an itinerant hole bound to a localized spin, similar to that proposed in the framework of the high-T$_c$ superconductors.[@zr] The low-energy properties of this metallic state can not be straightforwardly interpreted in terms of a single-band Hubbard model,[@sordi07; @sordi09] and it leads to remarkable properties.

A first partial indication of the anomalous nature of this state comes from an evaluation of the quasi-particle weight $Z=[1-\partial\Im\Sigma_f(i\o)/\partial\omega]_{|_{\omega\rightarrow0}}^{ -1}$, which measures the degree of metallicity of a system, being zero for a Mott insulator and one for a non-interacting metal. The results (see ) show that $Z$ is substantially smaller for the hole-doped than for the electron-doped case, already signaling that the Zhang-Rice liquid is a poorer metal than a standard correlated metal. In the following we will show that the difference goes well beyond the quasi-particle renormalization.

![(Color online) Main panel: imaginary part of the conduction electrons self-energy $\Im\Sigma_p(\iome)$ for increasing value of the hole doping and $T=0.001$. Data are from Lanczos ED calculations. Inset: Comparison of the $\Im\Sigma_p(\iome)$ behavior from different numerical methods for $\d=0.05$. The other model parameters are the same as in the main 