Illusive Many Body Localization
Lundi 15/11/2021, 16:00-17:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
It is believed that classical and most quantum short range integrable models are unstable to adding infinitesimal integrability breaking terms, i.e. that there is no KAM theorem in the thermodynamic limit. Quantum systems with disorder were thought to be an important exception from this rule, where it was argued that they remain non-ergodic at finite values of the interaction strength even in the thermodynamic limit. However, the story of MBL encountered several setback in the last few years. First, it was realized that it can not exist in dimensions larger than one. Even in one dimensional systems the lower bound for the transition point to the localized phase were pushed to much higher disorder than previously thought. In this talk I will argue that MBL is likely a transient phenomenon absent in the thermodynamic limit. Instead there is an essential singularity of conductivity near the infinite disorder strength, which cannot be captured by perturbative expansions. I will argue that most numerical results can be understood through studying a single impurity coupled to a bath where localization happens when the relaxation rate gets smaller than the level spacing. This is exactly the point, where Birkhoff perturbation theory for constructing local dressed integral of motion connected to the impurity spin starts to break down. I will argue that adding more impurities to the bath can at most double the system size where the system becomes ergodic.