Non-Hermitian Twisting Theory under the open boundary condition

• URL: http://arxiv.org/abs/2605.25386v1
• Date: Mon, 25 May 2026 03:29:08 GMT
• Title: Non-Hermitian Twisting Theory under the open boundary condition
• Abstract summary: We develop a site-resolved theory of the non-Hermitian skin effect (NHSE)<n>We extend non-Hermitian band theory to nonperiodic and disordered lattices.<n>Our results provide a universal paradigm for non-Hermitian physics in both crystalline and amorphous media.
• Score: 8.18061372368379
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The non-Hermitian skin effect (NHSE) is a hallmark of non-Hermitian system, yet its generalized Brillouin zone (GBZ) description is restricted to periodic systems. We develop a site-resolved theory via a local scaling transformation (LST), introducing local twisting $T_n$ to quantify metric operator $ξ$ nontriviality. This elucidates the NHSE's origin and uncovers the generalized multiple-channel skin effect (MCSE). Exploiting $T_n$'s translational independence, we define the Zahlen-Brillouin Zone (ZBZ), extending non-Hermitian band theory to nonperiodic and disordered lattices. Furthermore, we unify the $ξ$ with GBZ Riemannian geometry, establishing the metric and state correspondence (MSC) as the principle for real-space localization. With a global skin index $\mathbfΓ$ for phase transitions, our results provide a universal paradigm for non-Hermitian physics in both crystalline and amorphous media.

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