We consider the many-body localization-delocalization transition for strongly interacting one- dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transiti
ons at any finite temperature when varying the interaction strength. At weak interactions an increase in the interaction strength leads to insulator->fluid transition, and for large interactions one has a reentrance to the insulator regime.
We consider weakly interacting bosons in a 1D quasiperiodic potential (Aubry-Azbel-Harper model) in the regime where all single-particle states are localized. We show that the interparticle interaction may lead to the many-body delocalization and we
obtain the finite-temperature phase diagram. Counterintuitively, in a wide range of parameters the delocalization requires stronger cou- pling as the temperature increases. This means that the system of bosons can undergo a transition from a fluid to insulator (glass) state under heating.
