Strong electron correlations in geophysics

There is some fascinating solid state physics in geology, particularly associated with phase transitions between different crystal structures under high pressure. This provides some interesting examples and problems when teaching undergraduate thermodynamics. One of many nice features of the text by Schroeder is that it has discussions and problems associated with these phase transitions.

However, I would not have thought that the electronic transport properties, and particularly the role of electron correlations, would be that relevant to geophysics. But, I recently learnt this is not the case. A really basic unanswered question in geophysics is the origin and stability of the earths magnetic field due to the geodynamo. It turns out that the magnitude of the thermal conductivity of solid iron at high pressures and temperatures matters. One must consider not just the relative stability of different crystal structures but also the relative contributions of electron-phonon and electron-electron scattering to the thermal conductivity.

There is a nice preprint
Fermi-liquid behavior and thermal conductivity of ε-iron at Earth's core conditions 
L. V. Pourovskii, J. Mravlje, A. Georges, S.I. Simak, I. A. Abrikosov

They report results that contradict those of a recent Nature paper that has now been retracted.
A few minor observations stimulated by the paper.

a. This highlights the power and success of the marriage of Dynamical Mean-Field Theory (DMFT)  with electronic structure calculations based on Density Functional Theory (DFT) approximations. It impressive that people can now perform calculations to address such subtle issues as the relative stability and relative strength of electronic correlations in different crystal structures.

b. The disagreement between the two papers boils down to thorny issues associated with numerically performing the analytic continuation from imaginary time to real frequency. This is a whole can of worms that requires a lot of caution.

c. Subtle issues such as the value of the Lorenz ratio (Wiedemann-Franz law) for impurities compared to that for a Fermi liquid turn out to matter.

d. I have semantic issues about the use of the term "non-Fermi liquid" in both papers. The authors associate it with a resistivity (for high temperatures) that is not quadratic in temperature. The system still has quasi-particles that adiabatically connect to those in a non-interacting fermion system, and to me it is a Fermi liquid.