Many-Body Delocalization as a Quantum Avalanche

Thimothée Thiery, François Huveneers, Markus Müller, and Wojciech De Roeck
Phys. Rev. Lett. 121, 140601 – Published 2 October 2018
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Abstract

We propose a multiscale diagonalization scheme to study disordered one-dimensional chains, in particular, the transition between many-body localization (MBL) and the ergodic phase, expected to be governed by resonant spots. Our scheme focuses on the dichotomy of MBL versus validity of the eigenstate thermalization hypothesis. We show that a few natural assumptions imply that the system is localized with probability one at criticality. On the ergodic side, delocalization is induced by a quantum avalanche seeded by large ergodic spots, whose size diverges at the transition. On the MBL side, the typical localization length tends to the inverse of the maximal entropy density at the transition, but there is a divergent length scale related to the response to an inclusion of large ergodic spots. A mean-field approximation analytically illustrates these results and predicts a power-law distribution for thermal inclusions at criticality.

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  • Received 13 October 2017
  • Revised 31 August 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.140601

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Thimothée Thiery1,*, François Huveneers2,†, Markus Müller3,‡, and Wojciech De Roeck1,§

  • 1Instituut voor Theoretische Fysica, KU Leuven, 3001 Leuven, Belgium
  • 2Université Paris-Dauphine, PSL Research University, CNRS, CEREMADE, 75016 Paris, France
  • 3Paul Scherrer Institute, PSI, 5232 Villigen, Switzerland

  • *thimothee.thiery@kuleuven.be
  • huveneers@ceremade.dauphine.fr
  • markus.mueller@psi.ch
  • §wojciech.deroeck@kuleuven.be

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Issue

Vol. 121, Iss. 14 — 5 October 2018

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