Many-body localization (MBL) has emerged as a novel paradigm for ergodicity breaking in interacting systems subject to strong disorder.
In this talk, after a gentle introduction to the concepts of thermalizations and MBL, we will discuss MBL from the Fock-space perspective . We show that the MBL transition can be seen as a transition between ergodic states to non-ergodic extended states (multi-fractal). Furthermore, We demonstrate the non-self-averaging property of the many-body fractal dimension D_q and directly relate it to the jump of D_q as well as of the localization length of the integrals of motion at the MBL transition.
If time permits, in the last part of the talk, I will provide general bounds for the entanglement entropy for generic fractal many-body states .
 PRB104, 024202
 PRL 124, 200602 (2020)