  Recently many body localized systems have been treated as a hopping problem
on a Fock space lattice with correlated disorder, where the many-body
eigenstates exhibit multi-fractal character. The many-body propagator in Fock
space has been shown to be useful for capturing this multifractality and
extracting a Fock-space localization length for systems with random disorder in
real space. Here we study a one-dimensional interacting system of spinless
Fermions in the presence of a deterministic quasiperiodic potential using the
Fock-space propagator. From the system-size scaling of the self-energy
associated with the diagonal elements and the scaling of the off-diagonal
elements of the propagator, we extract fractal characteristics and FS
localization lengths, respectively, which behave similarly to that in the
random system. We compute the sample-to-sample fluctuations of the typical
self-energy and the off-diagonal propagator over different realizations of the
potential and show that the fluctuations in the self-energy distinguish
quasiperiodic and random systems, whereas the fluctuations of the off-diagonal
elements cannot demarcate the two types of potential.
