Microscopic Mechanism and Control of Reentrant Localization

Increasing quasiperiodic modulation can restore extended states after localization, raising the question of how the same modulation drives both localization and recovery. We identify a microscopic mechanism in quasiperiodic dimer chains by resolving scattering between Fourier channels. Specifically, scattering into neighboring channels and back shifts the spectral edge relative to a localization boundary determined by a neutral auxiliary resonance. Their successive crossings drive the same spectral packet with fixed integrated-density-of-states (IDS) labels into localization and back into an extended regime. This recovery persists across finite parameter ranges in both gap-opening families, including relative-phase detuning. Furthermore, an exact sublattice mapping enables compensated control of the recovery window and predicts recovery thresholds for individual IDS labels.