Non-Hermitian skin effect in a one-dimensional interacting Bose gas

Non-Hermitian skin effect (NHSE) is a unique feature studied extensively in noninteracting non-Hermitian systems. In this paper, we extend the NHSE originally discovered systems to interacting many-body by investigating an exactly solvable model, i.e., prototypical Lieb-Liniger Bose gas with imaginary vector potential. We show that model can also be solved through Bethe ansatz. By solving ansatz equations accurately, explicit eigenfunction obtained, and model's density profiles momentum distributions are calculated characterize quantitatively. find gradually suppressed on repulsive side but does not vanish as interaction strength increases. On attractive side, for bound-state solutions enhanced grows. contrast, scattering state shows nonmonotonic behavior side. Our paper provides example of systems, envision it extended other especially integrable models.