Localization Aspects In One Dimensional Driven Non-Hermitian Quasicrystals

Abstract

The phenomenon of localization of matter waves in condensed matter systems has been ubiquitous ever since its inception over sixty years ago. In this work, we study the delocalization-localization (DL) transition in two distinct non-equilibrium driven systems comprising of the static Hermitian and non-Hermitian Aubry-André-Harper (AAH) Hamiltonians on either realms of the drive. It is demonstrated that the systems with the former drive do not exhibit a sharp DL transition at the ‘critical point’, unlike its static constituents, in contrary to the systems governed by the latter driving protocol. However, the second devised non-Hermitian driven system becomes stabilized by virtue of the “extended unitarity”. Furthermore, we have found evidences that the former driven system manifests a multifractal nature in the localized regime, which is absent in the static quasicrystals of AAH type. To our mind, such unique localization and spectral features might be beneficial to experimentalists working in cold-atoms