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

TL;DR

This paper demonstrates the existence and behavior of the non-Hermitian skin effect in an exactly solvable interacting Bose gas model, revealing how interactions influence NHSE in many-body quantum systems.

Contribution

It extends the study of NHSE to an interacting many-body system, specifically the Lieb-Liniger Bose gas, and provides exact solutions and analysis of NHSE behavior with varying interactions.

Findings

NHSE is suppressed with increasing repulsive interaction.

NHSE is enhanced in attractive bound states as interaction grows.

NHSE exhibits non-monotonic behavior in attractive scattering states.

Abstract

Non-Hermitian skin effect (NHSE) is a unique feature studied extensively in non-interacting non-Hermitian systems. In this work, we extend the NHSE originally discovered in non-interacting 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 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 NSHE for bound-state solutions is enhanced as interaction strength grows. In contrast, for the scattering state the NHSE shows a non-monotonic behavior in the attractive side. Our work provides the first 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.