Hidden dualities in 1D quasiperiodic models*

We propose that Anderson localization-delocalization transitions in generic 1D quasiperiodic models are associated with local hidden duality symmetries. These symmetries are related with the Aubry-André duality through transformations that can be tackled by studying commensurate approximants of the target incommensurate system.
Based on this conjecture, we develop a method to compute critical points and duality transformations for generic quasiperiodic systems though their commensurate approximants. To illustrate the power of the method, mobility edges and duality symmetries are obtained for a number of models, including generalized Aubry-André models and coupled incommensurate chains.
Our findings provide a useful and insightful way to study Anderson transitions in quasiperiodic 1D systems, enabling the understanding of their emergence in generic models other than the Aubry-André model.