Localization–delocalization transition in the Generalized Aubry–André–Harper Model in a quasiperiodic superlattice potential

We investigate localization-delocalization transition in the one-dimensional generalized Aubry-André-Harper (GAAH) model in a quasiperiodic superlattice potential. The critical interplay between the model’s two modulated energy scales—the hopping amplitude ( t ) and the on-site potential ( Δ )—generates a rich phase diagram featuring extended, localized, and critical phases. We employ both static spectral and dynamics indicators to identify these phases. In static analysis, we compute the energy spectrum as a function of the common phase ϕ of the modulations and employ the inverse participation ratio (IPR) to map localization-delocalization phase diagram as a function of t and Δ . Dynamically, we model the evolution of an initially localized quantum state as a continuous-time quantum walk (CTQW), analyze the resulting probability distribution and time-dependent IPR to corroborate the static results. This work establishes a direct correspondence between static spectral indicators and dynamics, providing a unified framework for characterizing localization in quasiperiodic systems. Our findings offer new perspectives for controlling quantum transport in engineered quantum platforms. • Generalized Aubry–André–Harper model in an incommensurateoptical superlattice potential. • Topologically protected boundary states. • Extended, localized, and critical phases characterized by inverse participation ratio. • Single particle mobility edges. • Continuous-time quantum walks.