Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal

TL;DR

This paper introduces an exactly solvable non-Hermitian quasiperiodic model revealing a new critical phase where all eigenstates share identical multifractal properties, challenging traditional localization paradigms.

Contribution

It presents a novel non-Hermitian quasiperiodic lattice model with an analytically solvable critical phase exhibiting uniform multifractal eigenstates, expanding understanding of quasiperiodic criticality.

Findings

Discovered a non-Hermitian quasiperiodic critical phase with energy-independent eigenstates.

Mapped the system onto a disorder-free lattice via a nonunitary gauge transformation.

Established the persistence of this criticality in multiband lattices.

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.