Anomalous localization and duality in non-Hermitian quasiperiodic models

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 non-localized 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.

arXiv comment13 pages, 5figures