Informal Quantum Seminar: Vincent Grison (LPTMC Jussieu)

One-dimensional interacting bosons subjected to disorder are known to possess an insulating ground state, called the Bose glass. At finite temperature, perturbative computations advocate for a crossover to a non-disordered normal fluid, but an alternative scenario was also suggested, arguing for the existence of a genuine phase transition. The resulting low-temperature insulating phase is then akin to the Many-Body Localized (MBL) phase, first introduced for fermions.

To settle this debate, we develop a field-theoretical approach leveraging the Functional Renormalization Group (FRG). At zero temperature, we find a new non-perturbative fixed point, the approach to which contains information on the low-energy excitations of the system. We then turn to finite temperature effects, discussing various crossovers to the normal fluid phase, where disorder still plays an important role at finite length and time scales. Finally, we point out how a modification of our approximations leads to a different scenario for the low-temperature physics of the system, and put forward a hypothesis linking it to MBL.