Distinguishing localization from chaos: challenges in finite-size systems

Journal article

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 discuss a recent study (Šuntajs et al., 2020) of the behaviour of the Thouless energy and level repulsion in disordered spin chains, and its implications for the question of whether MBL is a true phase of matter.

Authors: Abanin, D; Bardarson, J; De Tomasi, G; Gopalakrishnan, S; Khemani, V

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Annals of Physics
• Volume: 427
• Issue: April 2021
• Article number: 168415
• Publication date: 2021-02-05
• Acceptance date: 2021-01-25
• DOI: 10.1016/j.aop.2021.168415
• ISSN: 0003-4916
• Language: English
• Keywords: strongly correlated electrons; localization; thouless energy; disordered systems; FFR; quantum chaos; many-body physics