Quantum Fisher Information of Localization Transitions in One-Dimensional Systems

Abstract

The concept of quantum Fisher information (QFI) is used to characterize the localization transitions in three representative one-dimensional models. It is found that the localization transition in each model can be distinctively illustrated by the evolution of QFI. For the Aubry-Andre model, the QFI exhibits an inflexion at the boundary between the extended states and localized ones. In the t 1−t 2 model, the QFI has a transition point separating the extended states from the localized states, while the mobility edge of the QFI is energy dependent. Furthermore, nine energy bands in the Soukoulis-Economou (S-E) model can be clearly revealed by the QFI with global mobility edges and local mobility edges. The present work demonstrates the implication of the QFI as a general fingerprint to characterize the localization transitions.