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