  The pseudogap phase occurring in cuprate and organic superconductors is
analyzed based on the dynamical cluster approximation (DCA) approach to the
Hubbard model. A cluster embedded in a self-consistent bath is studied. With
increasing Coulomb repulsion, U, the antinodal point [k=(pi,0)] displays a
gradual suppression of spectral density of states around the Fermi energy which
is not observed at the nodal point [k=(pi/2,pi/2)]. The opening of the
antinodal pseudogap is related to the internal structure of the cluster and the
much weaker bath-cluster couplings at the antinodal than nodal point. The role
played by internal cluster correlations is elucidated from a simple four-level
model. For small U, the cluster levels form Kondo singlets with their baths
leading to a peak in the spectral density. As U is increased a localized state
is formed localizing the electrons in the cluster. If this cluster localized
state is non-degenerate, the Kondo effect is destroyed and a pseudogap opens up
in the spectra at the anti-nodal point. The pseudogap can be understood in
terms of destructive interference between different paths for electrons hopping
between the cluster and the bath. However, electrons at the nodal points remain
in Kondo states up to larger U since they are more strongly coupled to the
bath. The strong correlation between the (pi,0) and (0,pi) cluster levels in
the localized state leads to a large correlation energy gain which is important
for localizing electrons and opening up a pseudogap. Such scenario is in
contrast with two independent Mott transitions found in two-band systems with
different bandwidths in which the localized cluster electron does not correlate
strongly with any other cluster electron for intermediate U. The important
intracluster sector correlations are associated with the resonating valence
bond (RVB) character of the cluster.
