Re-entrant single particle mobility edge in quasiperiodic chain

The single particle mobility edge (SPME) appears in the energy spectrum of a non-interacting quantum system as an energy separating the extended and the localized states. While the existence of the SPME is ruled out in the presence of a random disorder, its presence in certain types of one dimensional systems with quasiperiodic disorder has been established. The question is whether such an SPME is unique in a particular quantum system, or in other words, once the localization transition occurs whether the system remains localized forever? In our studies, we show that for a one dimensional dimerized lattice with staggered quasiperiodic disorder (having alternate signs across the lattice sites) there occurs a re-entrant localization phenomenon as a function of the disorder strength. We predict that for a range of the dimerization strength and beyond the localization transition, the SPME re-appears corresponding to larger values of the disorder strength, thereby resulting in more than one SPMEs in the system. By analyzing various physical quantities we concretely establish this re-entrant phenomena.