Anomalous localization and duality in non-Hermitian quasiperiodic models
Phys. Rev. B 114, 144205 – Published 24 September, 2026
DOI: https://doi.org/10.1103/dqsx-y2r3
Abstract
We develop a general framework based on the sign patterns of Lyapunov exponents for engineering and characterizing counterintuitive localization properties in one-dimensional non-Hermitian quasiperiodic lattices. On the one hand, for the Anderson localized states in the bulk under the periodic boundary condition, we find that their localization features can be boundary sensitive, becoming boundary-localized skin modes under the open boundary condition. On the other hand, for nonlocalized states, the well-known extended-localized duality relation can break down, as their counterparts in the dual model can also be nonlocal. We discuss how these remarkable phenomena can be understood from the perspective of Lyapunov exponents, highlighting the interplay of non-Hermiticiy and quasiperiodicity.
