Almost conserved operators in nearly many-body localized systems

Nicola Pancotti, Michael Knap, David A. Huse, J. Ignacio Cirac, and Mari Carmen Bañuls
Phys. Rev. B 97, 094206 – Published 23 March 2018

Abstract

We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.

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  • Received 18 October 2017
  • Revised 22 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.094206

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Nicola Pancotti1, Michael Knap2, David A. Huse3, J. Ignacio Cirac1, and Mari Carmen Bañuls1

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
  • 2Department of Physics and Institute for Advanced Study, Technical University of Munich, 85748 Garching, Germany
  • 3Physics Department, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 97, Iss. 9 — 1 March 2018

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