Reentrant localization transition in a one-dimensional quasiperiodic chain

We study the effects of an onsite quasiperiodic potential on the localization properties of a dimerized chain that may mimic the structure of a polymerized acetylene molecule.  An important ramification of the quasiperiodic potential is the presence of the mobility edge that segregates the energy spectrum between the localized and the delocalized phases. Interestingly, albeit stringent, for a specific assignment of the quasiperiodic potential where it alternates sign from one site to another (we refer it as a staggered scenario) and for a particular range of values for the dimerization strength, the system first undergoes a delocalization to localization transition corresponding to a certain value of the potential, which eventually gets into the delocalized phase again with further increase in the strength of the quasiperiodic potential. Thus, quite intriguingly, the system undergoes a re-entrant localization transition, a phenomenon that is unusual in electronic systems.  A further increase in the potential strength will eventually push the system into a completely localized phase. We believe that the re-entrant localization phenomena, which form the central focus of our work, are very specific to an interplay of the quasiperiodic potential and a dimerized hopping.