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  • Letter
  • Open Access

Multifractality and self-averaging at the many-body localization transition

Andrei Solórzano1, Lea F. Santos2, and E. Jonathan Torres-Herrera3

  • 1Tecnologico de Monterrey, Escuela de Ingeniera y Ciencias, Avenida Eugenio Garza Sada 2501, Monterrey, Nuevo Leon, Mexico, 64849
  • 2Department of Physics, Yeshiva University, New York, New York 10016, USA
  • 3Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, 72570, Puebla, Mexico

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Phys. Rev. Research 3, L032030 – Published 30 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032030

Abstract

Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this Letter, however, we discuss yet another crucial problem that has received much less attention, that of the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the noninteracting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

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Phys. Rev. Research 3, L032030– Published 30 July, 2021
  • Received 11 February 2021
  • Accepted 23 June 2021
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