Scaling of Fock space propagator in quasiperiodic many-body localizing systems

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. In particular, for the random system, the sample-to-sample fluctuations of the self-energy exhibits a distinct transition or sharp crossover within the thermal phase in the form of a peak whose height increases with system size. Such a feature is completely absent in the quasiperiodic system.