Mechanism for scale-free skin effect in one-dimensional systems

TL;DR

This paper proposes a model-independent mechanism for the scale-free skin effect in one-dimensional systems, enhancing understanding of finite size effects in non-Hermitian physics.

Contribution

It introduces a universal mechanism for SFSE in 1D systems, broadening the theoretical framework beyond specific models.

Findings

SFSE occurs in 1D Hermitian chains with imaginary impurities.

The mechanism explains size-dependent localization length in skin modes.

Provides new insights into finite size effects in non-Hermitian systems.

Abstract

Non-Hermitian skin effect (NHSE) is one of the most fascinating phenomena in non-Hermitian systems, which refers to enormous eigenstates localize at the boundary exponentially under open boundary condition (OBC). For typical NHSE, the localization length for a skin mode is independent of the system's size. Recently, some studies have revealed that for specific $1$-dimensional model, the localization length for eigenstates are proportional to the system's length under generalized boundary condition (GBC), and such phenomenon is dubbed as scale-free skin effect (SFSE). Further, SFSE is discovered in $1$-dimensional Hermitian chain with pure imaginary impurity at the end. In this work, we propose a mechanism for SFSE in 1-dimensional systems, which is model-independent. Our work provide a viewpoint for researching SFSE and shed new light on understanding finite size effect in non-Hermitian systems.