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

Timescale of local moment screening across and above the Mott transition