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

arXiv:2604.01638v2 Announce Type: replace Abstract: Non-Hermitian skin effect is one of the most captivating phenomena in non-Hermitian systems, characterized by the extensive localization of eigenstates near open boundaries. In its conventional form, the localization length of a skin mode is independent of the system size. Remarkably, however, when the open boundaries are coupled to realize a generalized boundary condition, the localization length can undergo a drastic transformation, becoming proportional to the system length. This intriguing regime is known as the scale-free skin effect (SFSE). Although SFSE has been observed in numerous one-dimensional non-Hermitian models through case-by-case studies, a unified theoret ical framework capable of predicting its emergence and characteristic properties remains absent. In this work, we take a firm step forward by establishing a model-independent framework for the ana lytic determination of scale-free localization lengths in certain regimes. Our key insight is to treat generalized boundary conditions as a perturbation of the periodic boundary conditions, thereby circumventing the singular response-to-perturbation that would otherwise arise if they were pertur batively treated relative to open boundary conditions. Our work sheds new light on understanding SFSE in non-Hermitian systems.

Abstract:Non-Hermitian skin effect is one of the most captivating phenomena in non-Hermitian systems, characterized by the extensive localization of eigenstates near open boundaries. In its conventional form, the localization length of a skin mode is independent of the system size. Remarkably, however, when the open boundaries are coupled to realize a generalized boundary condition, the localization length can undergo a drastic transformation, becoming proportional to the system length. This intriguing regime is known as the scale-free skin effect (SFSE). Although SFSE has been observed in numerous one-dimensional non-Hermitian models through case-by-case studies, a unified theoret ical framework capable of predicting its emergence and characteristic properties remains absent. In this work, we take a firm step forward by establishing a model-independent framework for the ana lytic determination of scale-free localization lengths in certain regimes. Our key insight is to treat generalized boundary conditions as a perturbation of the periodic boundary conditions, thereby circumventing the singular response-to-perturbation that would otherwise arise if they were pertur batively treated relative to open boundary conditions. Our work sheds new light on understanding SFSE in non-Hermitian systems.

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2604.01638 [quant-ph]

(or arXiv:2604.01638v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2604.01638 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

analiza aiqbench

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

Subiecte conexe