2017/06/30 by Thimothée Thiery, François Huveneers, Markus Müller +1 · 3 citations
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.121.140601
published as Phys. Rev. Lett. 121, 140601 (2018) · 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
arxiv created 2018/10/01 · arxiv updated 2018/10/10
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.