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-André 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.

Analytical treatment of Anderson localization in a chain of trapped ions experiencing laser Bessel beams

“…[17][18][19] Therefore, for the quasiperiodic model, critical values and mobility edges are very important issues and have attracted much attention. [19][20][21][22][23][24] In this paper, we investigate analytically the energydependent mobility edges and other characteristics regarding a quasiperiodic model using a chain of trapped ions confined stably and equidistantly in an anharmonic ion trap. [25] Trapped-ion systems can behave as non-interacting onedimensional lattices for quantum computation and quantum simulation, in which the vibrational degrees of freedom of the ions act as the data bus to transfer quantum information in the chain and entangle the separate ions.…”

Renormalization-group approach to quantum Fisher information in an XY model with staggered Dzyaloshinskii-Moriya interaction

“…In fact, earlier work 24 did prove the capability of the QFI in detecting the quantum criticality of the environment and this quantity does carry sufficient information on a lot of quantum phase transitions. Subsequently, we tested and then approved the QFI as a signature to characterize the localization transition of several one-dimensional quantum models 25 . Additionally, the scaling behaviors of QFI near the critical point of the XXZ spin chain model with the Dzyaloshinskii-Moriya (DM) interaction were discussed 26 , further demonstrating the QFI as a highly favorable measure of quantum information in a broad of quantum spin systems.…”