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We investigate the onset of a not-decaying asymptotic behavior of temporalmagnetic correlations in the Hubbard model in infinite dimensions. Thislong-term memory feature of dynamical spin correlations can be preciselyquantified by computing the difference between the zero-frequency limit of theKubo susceptibility and the corresponding static isothermal one. Here, wepresent a procedure for reliably evaluating this difference starting fromimaginary time-axis data, and apply it to the testbed case of the Mott-Hubbardmetal-insulator transition (MIT). At low temperatures, we find long-term memoryeffects in the entire Mott regime, abruptly ending at the first order MIT. Thisdirectly reflects the underlying local moment physics and the associateddegeneracy in the many-electron spectrum. At higher temperatures, a moregradual onset of an infinitely-long time-decay of magnetic correlations occursin the crossover regime, not too far from the Widom line emerging from thecritical point of the MIT. Our work has relevant algorithmic implications forthe analytical continuation of dynamical susceptibilities in stronglycorrelated regimes and offers a new perspective for unveiling fundamentalproperties of the many-particle spectrum of the problem under scrutiny.

Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis