  We study non-hermitian many-body physics in the interacting Hatano-Nelson
model with open boundary condition. The violation of reciprocity, resulting
from an imaginary vector potential, induces the non-hermitian skin-effect and
causes exponential localization for all single particle eigenfunctions in the
non-interacting limit. Nevertheless, the density profile of the interacting
system becomes only slightly tilted relative to the average filling. The
Friedel oscillations exhibit a beating pattern due to the modification of the
Fermi wavenumber. The probability distribution of particles over any finite
interval is the normal distribution, whose mean scales with the imaginary
vector potential and the variance is symmetric to the center of the chain. This
is confirmed by several numerically exact methods even for relatively small
systems. These features are expected to be generic not only for fermions, which
naturally repel each other due to Pauli's exclusion principle, but for
interacting bosons as well. Our findings indicate that many-body effects can
significantly alter and conceal the single particle properties and the skin
effect in non-hermitian systems.
