Distinguishing localization from chaos: challenges in finite-size systems
Abstract
We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we argue that a recent study [\v{S}untajs et al., arXiv:1905.06345] of the behavior of the Thouless energy and level repulsion in disordered spin chains likely reaches misleading conclusions, in particular as to the absence of MBL as a true phase of matter.
Keywords
Cite
@article{arxiv.1911.04501,
title = {Distinguishing localization from chaos: challenges in finite-size systems},
author = {D. A. Abanin and J. H. Bardarson and G. De Tomasi and S. Gopalakrishnan and V. Khemani and S. A. Parameswaran and F. Pollmann and A. C. Potter and M. Serbyn and R. Vasseur},
journal= {arXiv preprint arXiv:1911.04501},
year = {2021}
}
Comments
11 pages, 5 figures