s obtained from $G(\Vec{k},i\w_n)$ through the maximum-entropy method.

Figure \[fig:8site\] shows $A(\Vec{k}_\text{node},\w)$ for $t'=-0.2t$, $U=8t$, and $n=0.95$. The small but clear gap just above the Fermi level at $T=0.05t$ proves the fully-opened pseudogap.[@footnote4] The gap vanishes at a higher temperature $T=0.1t$. This is why the previous DCA study [@mj06] at a high temperature $T=0.12t$ did not observe the gap. Note that, a very recent study with 8-site DCA [@lg10] at $T=0.05t$ also detected a wispy reduction of the spectral weight at $\Vec{k}_\text{node}$ at low doping though the signal was so weak that it was not explicitly analyzed in their paper. The weakness of the signal would be due to the flat momentum dependence of the self-energy in each momentum patch in the DCA. Although the suppression of the spectrum is more subtle at higher doping in their result, it is reasonable because the pseudogap temperature decreases with doping.

The gap formation at the nodal point cannot be reproduced by the assumption of the $d$-wave pseudogap. We have confirmed this by employing the assumed form of the Green function employed in Ref. .

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