Understanding the origin of the pseudogap state in cuprate superconductors (and organic charge transfer salts) remains a challenge. It has now been shown that within a doped Hubbard or t-J model one can produce a pseudogap like state when the model is treated at the level of the Dynamical Cluster Approximation. The DCA is a generalisation of Dynamical Mean-Field Theory (DMFT) to small clusters. Although this is a significant advance it is still somewhat at the level of a "black box". One would like to know the essential physics.
Jaime Merino and Olle Gunnarsson have a preprint which shows how a two-site two-orbital model can capture some of the essential physics. This model is motivated by DCA calculations on the smallest four site cluster. The two orbitals correspond to (0,pi) and (pi,0) in the first Brillouin zone. Each orbital couples to an independent bath.
As U increases there is a transition from the cluster orbitals forming a Kondo singlet with the bath states to formation of a non-degenerate bound state on the cluster. The latter corresponds to formation of the pseudogap.
For larger clusters the coupling to the baths are much stronger for the nodal regions than the anti-nodal regions.