  The Hubbard model in $D$ dimensions, with the on-site repulsion $U$ and the
transfer integral between nearest neighbors $-t/\sqrt{D}$, is studied on the
basis of the Kondo-lattice theory. If $U/|t| \gg 1$, $|n - 1| \lesssim
|t|/(DU)$, where $n$ is the number of electrons per unit cell, and $D$ is so
small that $|J|/D \gg k_{\rm B}T_c$, where $J = -4t^2/U$ and $T_c$ is $0 {\rm
K}$ for $D = 1$ and is the highest critical temperature among possible ones for
$D \ge 2$, a low-$T$ phase where $T_c < T \ll |J|/(k_{\rm B}D)$ is a frustrated
electron liquid. Since the liquid is stabilized by the Kondo effect in
conjunction with the resonating-valence-bond (RVB) mechanism, it is simply the
RVB electron liquid; in one dimension, it is also the Tomonaga-Luttinger
liquid. The Kondo energy of the RVB liquid is $k_{\rm B}T_{\rm K} = O(|J|/D)$;
its effective Fermi energy is $O(k_{\rm B}T_{\rm K})$. A midband appears on the
chemical potential between the upper and lower Hubbard bands; the Hubbard gap
is a pseudogap. As regards the density of states per unit cell of the midband,
its bandwidth is $O(k_{\rm B}T_{\rm K})$ or $O(|J|/D)$, its peak height is
$O(1/U)$, and its spectral weight is $O[t^2/(DU^2)]$. Since the midband almost
disappears in the Heisenberg limit, the RVB electron liquid in the Heisenberg
limit is simply the RVB spin liquid. The RVB electron and spin liquids
adiabatically continue to each other. Since local moments form in a high-$T$
phase where $T \gtrsim T_{\rm K}$, the high-$T$ phase is simply the Mott
insulator.

Strongly Correlated Electrons