Control of localization in the non-Hermitian system

Non-Hermitian systems get lots of attention for studying open and dissipative quantum systems and their novel properties and applications in optics and condensed matter physics. One of the remarkable effects lies in the non-Hermitian skin effect which is the anomalous condensation of the bulk states at the edge resulting from non-reciprocal hopping magnitudes. From both theoretical and experimental points of view, it has been explored based on the Hatano-Nelson argument and topological exceptional points.

However, different types of non-Hermiticity have been barely studied and their characteristics remain elusive.

In this work, we focus on a non-Hermitian system where the hopping phase exists non-reciprocally and discuss the evolution of localization characteristics of the quantum states. We emphasize that the non-Hermiticity encoded in the hopping phase factor suppresses localization of the states in contrast to the non-Hermitian skin effect.

Furthermore, by quantifying the localization in the spectrum considering the inverse participation ratio and fractal dimension, we demonstrate that the non-Hermitian phase factor in the hopping terms controls the localization characteristics of the quantum states emergent in the quasicrystal. Our works offer the new types of non-Hermitian systems which are able to control of wave localization with various applications.