In this work, we demonstrate the coexistence of reentrant localization and dynamical delocalization in a one-dimensional non-Hermitian quasiperiodic lattice. Specifically, by considering a nonreciprocal dimerized lattice, we show that the additional off-diagonal quasiperiodic disorder can drive the system through two localization transitions as the disorder strength increases, a phenomenon that is absent in the corresponding reciprocal model. In this process, certain initially localized states are transformed back into extended states, leading to the emergence of a second critical region that holds the single-particle mobility edge. Interestingly, our investigation of the wave-packet dynamics reveals that within a part of the first initially localized region and the whole second localized region in the reentrant localization, the wave packet exhibits spatial spreading, also known as dynamical delocalization. This highly unusual behavior stems from the imaginary part (finite lifetime) of localized states during localization transitions. We validate these observations by analyzing participation ratios, the single-particle spectrum, finite-size analysis, and wave-packet evolution, culminating in a phase diagram that clearly delineates the phase transitions. Our work further enriches the understanding of reentrant localization phenomena and the associated wave-packet dynamics in quasiperiodic systems.

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• Anderson localization
• Disordered systems
• Quasicrystals
• Tight-binding model