paper

Many-body delocalization as a quantum avalanche

arXiv:1706.09338 · doi:10.1103/PhysRevLett.121.140601

Abstract

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. On the MBL side, the typical localization length tends to a finite universal value at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean field approximation analytically illustrates these results and predicts as a power-law distribution for thermal inclusions at criticality.

v2-->v3, accepted version (PRL) We stress the general picture, at the expense of the mean-field approximation. In particular, we prove a theorem stating, under minimal assumptions, that the density of thermal material is deterministic in the thermodynamic limit (even at criticality). We also prove a semicontinuitity result that suggests that the critical point is actually localized

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