Interplay of Quasiperiodic Criticality and the Non-Hermitian Skin Effect

• URL: http://arxiv.org/abs/2607.08294v1
• Date: Thu, 09 Jul 2026 09:38:40 GMT
• Title: Interplay of Quasiperiodic Criticality and the Non-Hermitian Skin Effect
• Abstract summary: Quasiperiodic lattices can host critical eigenstates, whereas nonreciprocal hopping in non-Hermitian lattices can induce non-Hermitian skin effect.<n>In this work, we investigate localization phenomena in a Hatano--Nelson model with quasiperiodically modulated hopping amplitudes.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quasiperiodic lattices can host critical eigenstates, whereas nonreciprocal hopping in non-Hermitian lattices can induce non-Hermitian skin effect. In this work, we investigate localization phenomena in a Hatano--Nelson model with quasiperiodically modulated hopping amplitudes, where nonreciprocity arises from unequal modulation strengths of the right and left hoppings. Using a non-unitary gauge transformation, we map the non-Hermitian system into a Hermitian quasiperiodic system and obtain an exact analytical expression for the Lyapunov exponent in the thermodynamic limit. Under periodic boundary conditions, inverse participation ratios and finite-size scaling analysis are used to identify the quasiperiodic critical regimes. The comparison shows that parameter regimes hosting quasiperiodic critical states under periodic boundary conditions can exhibit the non-Hermitian skin effect under open boundary conditions. Furthermore, the non-Hermitian skin effect associated with quasiperiodic critical regimes is also observed in representative long-range hopping models and multiband extensions. Our results provide an analytically controlled perspective on how quasiperiodicity, modulated nonreciprocity, and boundary conditions jointly shape the non-Hermitian skin effect in critical regimes.

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