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