But, I am not sure whether this picture is correct because as far as I am aware there are very few calculations of chi_s(omega), and particularly not its temperature dependence.
There are a few Dynamical Mean-Field Theory [DMFT] calculations at zero temperature, i.e., in the Fermi liquid regime, such as described here.
In the Mott insulating phase there is a delta function peak, associated with non-interacting local moments, as described here.
There are a few calculations in imaginary time, but little discussion of exactly what this means in real time. I struggle to make the connection.
The figure below shows a DMFT calculation of the imaginary time spin correlation function for the triangular lattice, by Jaime Merino, and reported in this PRB.
Here, I want to highlight two DMFT calculations for multi-band Hubbard models including Hund's rule coupling.
Spin freezing transition and non-Fermi-liquid self-energy in a three-orbital model
Philipp Werner, Emmanuel Gull, Matthias Troyer, Andy Millis
Dichotomy between Large Local and Small Ordered Magnetic Moments in Iron-Based Superconductors
P. Hansmann, R. Arita, A. Toschi, S. Sakai, G. Sangiovanni, and Karsten Held
The first paper reports the phase diagram below, where n is the average number of electrons per lattice site. The solid vertical lines represent a Mott insulating phase.
The important distinction is that in the Fermi liquid phase chi_s(tau beta=1/2) will go to zero linearly in temperature, whereas in the frozen moment regime it tends to a non-zero constant.
Similar results are obtained in the second paper, on a slightly different model, but they don't use the "frozen moment" language, and emphasise more the importance of the Hund's rule coupling.
Here, I have a basic question about the above results. The lowest temperature used in the Quantum Monte Carlo is T = t/100 [impressive], and so I wonder if this is above the Fermi liquid coherence temperature and if one could go to low enough temperatures one would recover a Fermi liquid.
It is known that the coherence temperature is often much smaller for two-particle properties, and Hund's rule can also dramatically lower it. Both points are discussed here.
Or is my question [bad metal vs. frozen moments] just a pedantic distinction? The important point is that, practically speaking, over a broad temperature range, the spins are effectively relaxing very slowly.
Anyway, I think there is some rich physics associated with spin dynamics in bad metals and hope it will be explored more in the next few years. I welcome discussion and particularly calculations!