of short-lived singlet-like electronic excitations.

![ $\s=\Im\Sigma_p(\iome\rightarrow0)$ as a function of the temperature for different values of the doping. The data shown are from full ED calculations. []{data-label="fig2.5"}](fig6.eps){width="45.00000%"}

To substantiate this discussion we study the evolution of the imaginary part of the conduction electron self-energy $\Im\Sigma_p(\iome)$. The results of our calculations for $\delta =0.1$ are presented in . A Fermi liquid state corresponds to a linear behavior of $\Im\Sigma_p(\iome)$ at low frequency, observed only at the lowest investigated temperature, $T=0.0005$. When we increase $T$ at values of the order of $T=0.0007$, two orders of magnitude smaller than the [*renormalized*]{} Fermi energy, the conduction-electron self-energy does not vanish in the $\omega \to 0$ limit, signaling a departure from the Fermi-liquid paradigm. Further increasing the temperature leads to an enhancement of this anomaly.

In we follow the evolution of $\Im\Sigma_p(\iome)$ for increasing doping at $T=0.001$. For small doping we have a clear NFL increase at small frequency which survives up to $\delta \simeq 0.16$. For larger doping the system is not strongly sensitive to the Mott-Hubbard physics and the standard Fermi-liquid behavior is restored around $\delta = 0.2$.

The violation of the Fermi-liquid paradigm can be summarized by the temperature dependence of 