Phase induced localization transition

Localization phenomenon is an important research field in condensed matter physics. However, due to the complexity and subtlety of disordered syestems, new localization phenomena always emerge unexpectedly. For example, it is generally believed that the phase of the hopping term does not affect the localization properties of the system, so the calculation of the phase is often ignored in the study of localization. Here, we introduce a quasiperiodic model and demonstrate that the phase change of the hopping term can significantly alter the localization properties of the system through detailed numerical simulations such as the inverse participation ratio and multifractal analysis. This phase-induced localization transition provides valuable information for the study of localization physics.