Many-body delocalization as a quantum avalanche

Understand

We propose a multi-scale diagonalization scheme to study disordered one-dimensional chains, in particular the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots.

• Our scheme focuses on the dichotomy MBL versus {ETH} (eigenstate thermalization hypothesis).
• We show that a few natural assumptions imply that the system is localized with probability one at criticality.
• On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition.