Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder

• URL: http://arxiv.org/abs/2507.05691v1
• Date: Tue, 08 Jul 2025 05:56:10 GMT
• Title: Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Authors: Shu Long, Linhu Li,
• Abstract summary: We investigate two weakly coupled non-Hermitian Hatano-Nelson chains under M"obius boundary conditions.<n>We find that eigenstates exhibit non-Hermitian skin effect in one chain and scale-free localization in the other.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Non-Hermitian systems possess exotic localization phenomena beyond their Hermitian counterparts, exhibiting massive accumulation of eigenstates at the system boundaries with different scaling behaviors. In this study, we investigate two weakly coupled non-Hermitian Hatano-Nelson chains under M\"obius boundary conditions (MBCs), and reveal the coexistence of two distinct localization behaviors for eigenstates. Namely, eigenstates exhibit non-Hermitian skin effect in one chain and scale-free localization in the other. Notably, the localization characteristics of eigenstates can exchange between the two chains depending on their eigenenergies. This phenomenon is found to emerge from the critical behaviors induced by the weak interchain coupling, which can even be enhanced by MBCs in comparison \red{to} the system under other boundary conditions. Our findings deepen the understanding of non-Hermitian localization and criticality, and offer new insights into engineering tunable edge-localized states in synthetic quantum systems.

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