The long road from the Hubbard model to experiment

An outstanding theoretical challenge remains (reliably) calculating thermodynamic and transport properties of the one band Hubbard model. This is necessary to answer questions such as: is it the relevant effective Hamiltonian for cuprate superconductors?

Emanuel Gull gave a nice talk at the conference about work on cluster DMFT treatment of the doped Hubbard model. This PRB paper contains a nice comparison of how the results vary with cluster size.  They consider cluster geometries up to 16 sites. At least 8 sites are necessary to cover the important region around wavevector (pi/2,pi/2) where one hopes to find nodes in a pseudogap, superconducting gap, and cold spots on the Fermi surface.
The calculations produce four distinct phases:

• Mott insulator
• An isotropic Fermi liquid (FL)
• A FL with momentum space differentiation
• A momentum selective Mott insulator (a pseudogap state)

Of particular interest to me is the existence of the third state which may correspond to the anisotropic Marginal Fermi liquid state seen in overdoped cuprates. It is desirable to compare the doping, temperature, and frequency dependences of the self energies they calculate [Figures 8-11] to the model form that Jure Kokalj and I have considered.