Certain General Constraints on the Many-Body Localization Transition

Isolated quantum systems at strong disorder can display many-body localization (MBL), a remarkable phenomena characterized by an absence of conduction even at finite temperatures. As the ratio of interactions to disorder is increased, one expects that an MBL phase will eventually undergo a dynamical phase transition to a delocalized phase. Here we constrain the nature of such a transition by exploiting the strong subadditivity of entanglement entropy, as applied to the many-body eigenstates close to the transition in general dimensions. In particular, we show that at a putative continuous transition between an MBL and an ergodic delocalized phase, the critical eigenstates are necessarily thermal, and therefore, the critical entanglement entropy equals the thermal entropy. We also explore a qualitatively different continuous localization-delocalization transition, where the delocalized phase is non-ergodic whose volume law entanglement entropy tends to zero as the transition is approached.