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arXiv · 2601.23015

Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal

Zhangyuan Chen·Muhammad Idrees·Ying Yang·Xianqi Tong·Xiaosen Yang
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Abstract

Critical states in quasiperiodic systems defy the conventional dichotomy between extended and localized states. In this work, we demonstrate that non-Hermiticity fundamentally reshapes this paradigm by giving rise to an exactly solvable quasiperiodic critical phase with no energy selectivity. We introduce a non-Hermitian quasiperiodic lattice based on a modulated Hatano-Nelson model and uncover a new universality class of quasiperiodic skin criticality, in which all eigenstates share an identical multifractal spatial structure. Through a nonunitary gauge transformation, the system is mapped onto a disorder-free lattice, enabling exact analytical solutions for the full spectrum and eigenstates. As a consequence, the inverse participation ratio is strictly energy-independent and controlled solely by a global phase. We further show that this criticality persists in multiband lattices, establishing a general and analytically controlled framework for non-Hermitian quasiperiodic critical phenomena.

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Zhangyuan Chen, Muhammad Idrees, Ying Yang, Xianqi Tong, Xiaosen Yang. 2026-01-30. Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal. https://doi.org/10.1103/wlsw-zyq9

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