Thouless Time Analysis of Anderson and Many-Body Localization Transitions

Piotr Sierant, Dominique Delande, and Jakub Zakrzewski
Phys. Rev. Lett. 124, 186601 – Published 7 May 2020
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Abstract

Spectral statistics of disordered systems encode Thouless and Heisenberg timescales, whose ratio determines whether the system is chaotic or localized. We show that the scaling of the Thouless time with the system size and disorder strength is very similar in one-body Anderson models and in disordered quantum many-body systems. We argue that the two parameter scaling breaks down in the vicinity of the transition to the localized phase, signaling a slowing-down of dynamics.

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  • Received 15 November 2019
  • Revised 11 February 2020
  • Accepted 13 April 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.186601

© 2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Piotr Sierant1,*, Dominique Delande2, and Jakub Zakrzewski1,3

  • 1Institute of Theoretical Physics, Jagiellonian University in Krakow, Łojasiewicza 11, 30-348 Kraków, Poland
  • 2Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 Place Jussieu, 75005 Paris, France
  • 3Mark Kac Complex Systems Research Center, Uniwersytet Jagielloński, 30-348 Kraków, Poland

  • *piotr.sierant@uj.edu.pl

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Issue

Vol. 124, Iss. 18 — 8 May 2020

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