Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal

• URL: http://arxiv.org/abs/2601.23015v1
• Date: Fri, 30 Jan 2026 14:26:14 GMT
• Title: Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Authors: Zhangyuan Chen, Muhammad Idrees, Ying Yang, Xianqi Tong, Xiaosen Yang,
• Abstract summary: Critical states in quasiperiodic systems defy the conventional dichotomy between extended and localized states.<n>We introduce a non-Hermitian quasiperiodic lattice based on a Hatano-Nelson model.<n>We show that this criticality persists in multiband lattices, establishing a general and analytically controlled framework.
• Score: 1.3594185103430554
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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