We unveil an exotic phenomenon arising from the intricate interplay between
non-Hermiticity and many-body physics, namely an occupation-dependent particle
separation for hardcore bosons in a one-dimensional lattice driven by
uni-directional non-Hermitian pumping. Taking hardcore bosons as an example, we
find that a pair of particles occupying the same unit cell exhibit an opposite
non-Hermitian pumping direction to that of unpaired ones occupying different
unit cells. By turning on an intracell interaction, many-body eigenstates split
in their real energies, forming separable clusters in the complex energy plane
with either left-, right-, or bipolar-types of non-Hermitian skin effect
(NHSE). The dependency of skin accumulating directions on particle occupation
is further justified with local sublattice correlation and entanglement entropy
of many-body eigenstates. Dynamically, this occupation-dependent NHSE manifests
as uni- or bi-directional pumping for many-body initial states, allowing for
spatially separating paired and unpaired particles. Similar phenomena also
apply to fermionic systems, unveiling the possibility of designing and
exploring novel non-Hermitian phases originated from particle non-conservation
in subsystems (e.g., orbitals, sublattices, or spin species) and their spatial
configurations.Comment: 18pages, 14 fiugre