Timescale of local moment screening across and above the Mott transition

A material's phase diagram typically indicates the types of realized long-range orders, corresponding to instabilities in static response functions. In correlated systems, however, key phenomena crucially depend on dynamical processes, too: In a Mott insulator, the electrons' spin moment fluctuates in time, while it is dynamically screened in Kondo systems. Here, we introduce a timescale $t_m$ characteristic for the screening of the local spin moment and demonstrate that it fully characterizes the dynamical mean-field phase diagram of the Hubbard model: The retarded magnetic response delineates the Mott transition and provides a new perspective on its signatures in the supercritical region above. We show that $t_m$ has knowledge of the Widom line and that it can be used to demarcate the Fermi liquid from the bad metal regime. Additionally, it reveals new structures inside the Fermi liquid phase: First, we identify a region with preformed local moments that we suggest to have a thermodynamic signature. Second, approaching the Mott transition from weak coupling, we discover a regime in which the spin dynamics becomes adiabatic, in the sense that it is much slower than valence fluctuations. Our findings provide resolution limits for magnetic measurements and may build a bridge to the relaxation dynamics of non-equilibrium states.