Re-entrant localization transitions in quasi-periodic lattices

The phenomenon of localization of quantum states of electrons in random lattices known as the Anderson localization has been the topic of paramount interest in condensed matter physics. While the Anderson localization transition is possible in higher dimensions, in one and two dimensional cases, quantum states become localized for any arbitrary small disorder. However, systems with quasiperiodic disorder are known to exhibit a localization transition in low dimensions. i.e. after a critical strength of disorder, all the states of the system become localized. In this talk we will show that in a one-dimensional dimerized lattice with quasiperiodic disorder, there exists two localization transitions as a function of quasi-periodic disorder. This means, after the first localization transition, some of the localized eigenstates become extended for a range of intermediate disorder strengths. Eventually, the system undergoes a second localization transition at a higher disorder strength. We will further focus on other quasi periodic lattices where the re-entrant localization transitions can occur. In the end, we will discuss the possible experimental signatures of the re-entrant localization transition in the wavepacket dynamics.