Liouvillian skin effect in a one-dimensional open many-body quantum system with generalized boundary conditions

TL;DR

This paper introduces the Liouvillian skin effect (LSE) in one-dimensional open quantum many-body systems, demonstrating its boundary-condition sensitivity and providing an exactly solvable model using Bethe ansatz to analyze its properties.

Contribution

It identifies and characterizes the Liouvillian skin effect in dissipative quantum systems with generalized boundary conditions, using an exactly solvable model.

Findings

LSE exists under certain boundary conditions.

LSE is sensitive to boundary modifications.

LSE can be fragile or robust depending on boundary hopping.

Abstract

Non-Hermitian skin effect (NHSE), namely that eigenstates of non-Hermitian Hamiltonains are localized at one boundary in the open boundary condition, attracts great interest recently.In this paper, we investigate the skin effect in one-dimensional dissipative quantum many-body systems, which we call the Liouvillian skin effect (LSE). We rigorously identify the existence of LSE for generalized boundary conditions by solving the Liouvillian superoperator of an exactly solvable model with the advantage of Bethe ansatz. The LSE is sensitive to boundary conditions where the signature is reflected in eigenfunctions of the system. We confirm that the LSE is fragile to a tiny co-flow boundary hopping with non-Hermitian current but can survive for a counter-flow boundary hopping in the thermodynamic limit. Our work provides a prototypical example of exactly solvable dissipative quantum many-body lattice systems exhibiting LSE for generalized boundary conditions. It can be further extended to other integrable open quantum many-body models.