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We supplement the determinantal and Pfaffian bounds of Sims and Warzel(Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-freefermions, by considering the high dimensional case and complex-timecorrelations. Our proof uses the analyticity of correlation functions via theHadamard three-line theorem. We show that the dynamical localization for theone-particle system yields the dynamical localization for the many-pointfermionic correlation functions, with respect to the Hausdorff distance in thedeterminantal case. In Sims and Warzel (2016), a stronger notion of decay formany-particle configurations was used but only at dimension one and for realtimes. Considering determinantal and Pfaffian correlation functionals forcomplex times is important in the study of weakly interacting fermions.

Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices