N. J. B. Aza, J.-B. Bru, W. de Siqueira Pedra
Decay of Complex-time Determinantal Correlation Functionals in Lattices
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ABSTRACT. We supplement the determinantal bounds of [4] for many-body
localization of free fermions, by considering the high dimensional case and complex-time correlations. Our proof uses the analyticity of correlation functions via the Hadamard three-lines 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 [4], a stronger notion of decay for many-particle configurations was used but only at dimension one and for real times. Considering determinantal correlation functionals for complex times is important in the study of weakly interacting fermions.