Distinguishing localization from chaos: Challenges in finite-size systems

D. A. Abanin, J. H. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. A. Parameswaran, F. Pollmann, A. C. Potter, M. Serbyn, R. Vasseur

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


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.

Original languageEnglish (US)
Article number168415
JournalAnnals of Physics
StatePublished - Apr 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Disordered systems
  • Localization
  • Many-body physics
  • Quantum chaos
  • Strongly correlated electrons
  • Thouless energy


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