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Measurement-induced disturbance near Anderson localization in one-dimensional systems

We study the localization transition in several typical one-dimensional single-particle systems by means of measurement-induced disturbance (MID). The results show that the MID presents a rapid drop around the boundary between the localized state and extended ones, and the corresponding first-order derivative exhibits a behavior of divergence around the critical point for deterministic on-site potential systems (e.g. the quasi-periodic model). These characteristics can capture a phase diagram as well as the traditional method. For the non-deterministic on-site systems (e.g. the random dimer model), the states around the resonant energies possess relatively large values for MID, which means that they are extended. In addition, as the random potential ϵ b exceeds the critical value, the states possessing a large MID vanish completely. These results show that MID can be useful in detecting localization transition in these typical one-dimensional systems.