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Quantum logarithmic multifractality

Weitao Chen1,2,3, Olivier Giraud2,3,4, Jiangbin Gong1,2,3,*, and Gabriel Lemarié2,3,5,†

  • *Contact author: phygj@nus.edu.sg
  • †Contact author: lemarie@irsamc.ups-tlse.fr
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Phys. Rev. Research 6, L032024 – Published 31 July, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032024

Abstract

Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed “logarithmic multifractality,” in effectively infinite-dimensional systems undergoing the Anderson transition. In contrast to conventional multifractality observed in finite dimensions, logarithmic multifractality at infinite dimension introduces an algebraic behavior with respect to the logarithm of system size or time. We demonstrate this phenomenon across eigenstate statistics, spatial correlations, and wave packet dynamics. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition, such as the many-body localization transition.

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Describing the critical behavior of the Anderson transition in infinite dimension by random-matrix ensembles: Logarithmic multifractality and critical localization

Weitao Chen, Olivier Giraud, Jiangbin Gong, and Gabriel Lemarié
Phys. Rev. B 110, 014210 (2024)

Article Text

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Phys. Rev. Research 6, L032024– Published 31 July, 2024
  • Received 29 December 2023
  • Accepted 25 June 2024
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