Closing the gaps in our understanding

As we struggle to understand the pseudogap state in the cuprate superconductors any successful theory must be able to describe at least qualitatively a few key features:

• the d-wave symmetry
• the existence of Fermi arcs which increase in length with doping
• well-defined quasi-particles near the nodes
  
• incoherent excitations near the anti-nodes

Can a one-band Hubbard model capture such features?

Furthermore, if it can, is there a "simple" physical picture of the underlying physics?

I believe that affirmative answers to both questions are given in a very nice preprint by Ferrero, Cornaglia, De Leo, Parcollet, Kotliar, and Georges.

Some of the results were published earlier in PRL, which contains the nice figure below of
the spectral function at the chemical potential at different doping away from half filling.

This work builds on the successes of Kotliar and Georges at developing Cluster Dynamical Mean-Field Theory (DMFT), rotationally invariant slave boson theory, and orbital-selective Mott transitions.

They divide momentum space into just two regions and consider the associated two-site DMFT. Symmetric and anti-symmetric combinations of the two sites correspond to the nodal and anti-nodal regions, respectively.
Formation of the pseudogap is associated with a Mott transition in the anti-symmetric orbital. The different behaviours of the two orbitals (momentum regions) is due to the formation of inter-site spin singlets. They compare the essential physics to that which occurs in the two-impurity Anderson model. In that case there is competition when formation of a singlet between the two impurities and two separate Kondo singlets between
each of the impurity spins and the itinerant electrons.

The calculations agree well with STM and ARPES experiments.