Localization transition, spectrum structure, and winding numbers for one-dimensional non-Hermitian quasicrystals

By analyzing the Lyapunov exponent, the authors develop here a general scheme for the study of one-dimensional non-Hermitian quasicrystals. Based on Avila's global theory, they establish a correspondence between a series of non-Hermitian quasicrystals and their corresponding Hermitian models, which allows them to obtain the phase transition properties of non-Hermitian systems just by studying the corresponding Hermitian cases. They also unveil an intriguing feature in the robust spectrum and the intrinsic relation between the winding number and slope of the Lyapunov exponent.