Size-dependent critical localization

Hui-Qiang Liang; Linhu Li; Guo-Fu Xu

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arXiv · 2509.18943

Size-dependent critical localization

Hui-Qiang Liang·Linhu Li·Guo-Fu Xu

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Abstract

Studying critical states in quasiperiodic systems is of great importance in localization physics. Previously identified critical states share a common characteristic: they exhibit persistent critical features in the thermodynamic limit. In this Letter, we predict an exotic type of critical state, termed size-dependent critical states, which exhibit a fundamentally distinct behavior. Specifically, they display critical localization signatures only at finite sizes, but transition to Anderson localization in the thermodynamic limit. We establish that the physical origin of size-dependent critical states lies in the synergistic interplay between local non-reciprocal domain wall and NHSE. By revealing a critical phase that challenges the established paradigm of critical localization, our work opens new avenues for exploring localization phenomena in quasiperiodic systems.

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Hui-Qiang Liang, Linhu Li, Guo-Fu Xu. 2025-09-23. Size-dependent critical localization. https://arxiv.org/abs/2509.18943

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