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Subdiffusion in the Anderson model on the random regular graph

Giuseppe De Tomasi, Soumya Bera, Antonello Scardicchio, and Ivan M. Khaymovich
Phys. Rev. B 101, 100201(R) – Published 3 March 2020
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Abstract

We study the finite-time dynamics of an initially localized wave packet in the Anderson model on the random regular graph (RRG) and show the presence of a subdiffusion phase coexisting both with ergodic and putative nonergodic phases. The full probability distribution Π(x,t) of a particle to be at some distance x from the initial state at time t is shown to spread subdiffusively over a range of disorder strengths. The comparison of this result with the dynamics of the Anderson model on Zd lattices, d>2, which is subdiffusive only at the critical point implies that the limit d is highly singular in terms of the dynamics. A detailed analysis of the propagation of Π(x,t) in space-time (x,t) domain identifies four different regimes determined by the position of a wave front Xfront(t), which moves subdiffusively to the most distant sites Xfront(t)tβ with an exponent β<1. Importantly, the Anderson model on the RRG can be considered as proxy of the many-body localization transition (MBL) on the Fock space of a generic interacting system. In the final discussion, we outline possible implications of our findings for MBL.

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  • Received 11 September 2019
  • Revised 20 December 2019
  • Accepted 10 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.100201

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Giuseppe De Tomasi1,2,*, Soumya Bera3, Antonello Scardicchio4,5, and Ivan M. Khaymovich6

  • 1Department of Physics, T42, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany
  • 2T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 3Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
  • 4Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
  • 5INFN, Sezione di Trieste, Via Valerio 2, 34126 Trieste, Italy
  • 6Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany

  • *gd453@cam.ac.uk

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Issue

Vol. 101, Iss. 10 — 1 March 2020

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