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Stability and instability towards delocalization in many-body localization systems

Wojciech De Roeck and François Huveneers
Phys. Rev. B 95, 155129 – Published 18 April 2017

Abstract

We propose a theory that describes quantitatively the (in)stability of fully many-body localization (MBL) systems due to ergodic, i.e., delocalized, grains, that can be, for example, due to disorder fluctuations. The theory is based on the ETH hypothesis and elementary notions of perturbation theory. The main idea is that we assume as much chaoticity as is consistent with conservation laws. The theory describes correctly—even without relying on the theory of local integrals of motion (LIOM)—the MBL phase in one dimension at strong disorder. It yields an explicit and quantitative picture of the spatial boundary between localized and ergodic systems. We provide numerical evidence for this picture. When the theory is taken to its extreme logical consequences, it predicts that the MBL phase is destabilised in the long time limit whenever (1) interactions decay slower than exponentially in d=1 and (2) always in d>1. Finer numerics is required to assess these predictions.

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  • Received 1 September 2016
  • Revised 5 February 2017

DOI:https://doi.org/10.1103/PhysRevB.95.155129

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Wojciech De Roeck1 and François Huveneers2

  • 1Instituut voor Theoretische Fysica, KU Leuven, 3001 Leuven, Belgium
  • 2Université Paris-Dauphine, PSL Research University, CNRS, CEREMADE, 75016 Paris, France

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Issue

Vol. 95, Iss. 15 — 15 April 2017

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