Geometric Signatures of Localization Transitions

Information-theoretic approaches offer a powerful framework for probing subtle variations in quantum states. We show that the Fisher Information Matrix (FIM) provides a sensitive and geometric probe of localization-delocalization transitions in one-dimensional quasiperiodic tight-binding models with multiple independent parameters. In systems exhibiting reentrant localization, the FIM not only accurately identifies the transition points but also reveals subtle structural features of the wavefunctions that conventional measures fail to capture. Our results establish the FIM as a powerful tool for characterizing criticality and the geometry of quantum states in complex quasiperiodic models.