panel. The QMC and full ED calculations are performed at $T=0.008$. DMRG is a $T=0$ calculation performed with a cluster of $N_{\rm s}=30$ sites and plotted down to the position of the lowest energy pole.[]{data-label="fig2.4"}](fig5.eps){width="45.00000%"}

Thermal breakdown of the Fermi-liquid {#sec3}
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Fermi-liquid theory is the standard paradigm for metallic systems and describes correlated Fermi systems as a collection of non-interacting renormalized quasi-particles. DMFT studies of various correlated models have shown that even very close to the Mott transition the correlated metallic state is typically a Fermi liquid with a reduced effective hopping proportional to the quasi-particle weight $Z$. This scale also controls the coherence temperature above which the coherent motion of the carriers is destroyed by thermal fluctuations.

In this section we will show that the correlated metallic state of the PAM in the weakly hole-doped regime turns out to be very fragile with respect to small temperatures. More precisely, our system will be a Fermi liquid only below an extremely small coherence temperature which, for small doping, can be substantially smaller than the renormalized Fermi energy controlled by $Z$. Therefore the corresponding metallic state can not be described in terms of long-lived quasi-particles but is rather a liquid 