The main question that the talk is trying to address is: what is the origin of the low temperature coherence scale T_coh associated with the crossover from a bad metal to a Fermi liquid?
In particular, T_coh is much less than the Fermi temperature of for non-interacting band structure of the relevant Hubbard model [on an anisotropic triangular lattice at half filling].
Here is the key figure from the talk [and the PRL written with Jure Kokalj].
It shows the temperature dependence of the specific heat for different values of U/t for a triangular lattice t'=t. Below T_coh, the specific heat becomes approximately linear in temperature. For U=6t, which is near the Mott insulator transition, T_coh ~t/20. Thus, we see the emergence of the low energy scale.
Note that well into the Mott phase [U=12t] there is a small peak in the specific heat versus temperature. This is also seen in the corresponding Heisenberg model and corresponds to spin-waves associated with short-range antiferromagnetic order.
So here are the further questions.
What is the effect of frustration?
How does T_coh compare to the antiferromagnetic exchange J=4t^2/U?
The answers are in the Supplementary material of PRL. [I should have had them as back-up slides for the talk]. The first figure shows the specific heat for U=10t and different values of the frustration.
t'=0 [red curve] corresponds to the square lattice [no frustration] and t'=t [green dot-dashed curve] corresponds to the isotropic triangular lattice.
The antiferromagnetic exchange constant J=4t^2/U is shown on the horizontal scale. For the square lattice there is a very well defined peak at temperature of order J. However, as the frustration increases the magnitude of this peak decreases significantly and shifts to a much lower temperature.
This reflects that there are not well-defined spin excitations in the frustrated system.
The significant effect of frustration is also seen in the entropy versus temperature shown below. [The colour labels are the same]. At low temperatures frustration greatly increases the entropy, reflecting the existence of weakly interacting low magnetic moments.