I am often sprucing [Aussie slang for promoting] Dynamical Mean Field Theory (DMFT), and particularly how it captures many quantitative details of charge transport and bad metals in organic charge transfer salts.
However, it is always good and important to be transparent about the limitations of any theory, particularly one that you are enthusiastic about.
There is a nice paper
Repulsive versus attractive Hubbard model: Transport properties and spin-lattice relaxation rate
Rok Žitko, Žiga Osolin, and Peter Jeglič
The authors use DMFT to calculate various spectral functions using the numerical renormalisation group (NRG) as the impurity solver. This is probably, the most reliable method, at least for low temperatures.
There is a lot I found interesting in the paper. But for now I just want to focus on one result in the paper: the temperature dependence of the NMR relaxation rate, 1/T_1.
1/(T_1 T) is proportional to the slope of the local spin fluctuation spectral function
Jarrell and Pruschke.
Why is this interesting?
In the organic charge transfer salts 1/T1T versus temperature is not monotonic, but has a maximum at a temperature (T_NMR) around the coherence temperature, T_coh, marking the approximate crossover from a bad metal (at high temperatures) to a Fermi liquid (at low temperatures). Actual data for a wide range of materials is shown in the Figure below, (n.b. this is a plot of T_1 T vs. T not 1/T_1T) taken from a paper, with Ben Powell and Eddy Yusuf.
But, it was good to be reminded of it again.
What is going on?
Basically, like in the cuprates a pseudogap must be opening up. A cluster DMFT calculation, such as this one by Jaime Merino and Olle Gunnarsson [or one by Emanuel Gull ] captures this.
But, it remains to be shown in detail that the NMR data can be quantitatively described and the relationship between the two temperature scales T_coh and T_NMR needs to be elucidated.