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

• URL: http://arxiv.org/abs/2604.01638v1
• Date: Thu, 02 Apr 2026 05:25:58 GMT
• Title: Mechanism for scale-free skin effect in one-dimensional systems
• Abstract summary: Non-Hermitian skin effect refers to enormous eigenstates localize at the boundary exponentially under open boundary condition (OBC)<n>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)<n>In this work, we propose a mechanism for SFSE in 1-dimensional systems, which is model-independent.
• Score: 0.30458514384586394
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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