  Localization in one-dimensional interacting systems can be caused by disorder
potentials or non-Hermiticity. The former phenomenon is the many-body
localization (MBL), and the latter is the many-body non-Hermitian skin effect
(NHSE). In this work, we numerically investigate the interplay between these
two kinds of localization, where the energy-resolved MBL arises from a
deterministic quasiperiodic potential in a fermionic chain. We propose a set of
eigenstate properties and long-time dynamics that can collectively distinguish
the two localization mechanisms in the presence of non-Hermiticity. By
computing the proposed diagnostics, we show that the thermal states are
vulnerable to the many-body NHSE while the MBL states remain resilient up to a
strong non-Hermiticity. Finally, we discuss experimental observables that can
probe the difference between the two localizations in a non-Hermitian
quasiperiodic fermionic chain. Our results pave the way toward experimental
observations on the interplay of interaction, quasiperiodic potential, and
non-Hermiticity.
