  Non-Hermiticity gives rise to unique topological phases that have no
counterparts in Hermitian systems. Such intrinsic non-Hermitian topological
phases appear even in one dimension while no topological phases appear in
one-dimensional Hermitian systems. Despite the recent considerable interest,
the intrinsic non-Hermitian topological phases have been mainly investigated in
noninteracting systems described by band theory. It has been unclear whether
they survive or reduce in the presence of many-body interactions. Here, we
demonstrate that the intrinsic non-Hermitian topological phases in one
dimension survive even in the presence of many-body interactions. We formulate
a many-body topological invariant by the winding of the complex-valued
many-body spectrum in terms of a U (1) gauge field (magnetic flux). As an
illustrative example, we investigate the interacting Hatano-Nelson model and
find a unique topological phase and skin effect induced by many-body
interactions.
