Spectral features of a many-body-localized system weakly coupled to a bath

Rahul Nandkishore, Sarang Gopalakrishnan, and David A. Huse
Phys. Rev. B 90, 064203 – Published 27 August 2014

Abstract

We study many-body-localized (MBL) systems that are weakly coupled to thermalizing environments, focusing on the spectral functions of local operators. These spectral functions carry signatures of localization even away from the limit of perfectly isolated systems. We find that, in the limit of vanishing coupling to a bath, MBL systems come in two varieties, with either discrete or continuous local spectra. Both varieties of MBL systems exhibit a “soft gap” at zero frequency in the spatially averaged spectral functions of local operators, which serves as a diagnostic for localization. We estimate the degree to which coupling to a bath broadens these spectral features, and we find that some characteristics of incipient localization survive as long as the system-bath coupling is much weaker than the characteristic energy scales of the system. We discuss the crossover to localization that occurs as the coupling to the external bath is tuned to zero. Since perfect isolation is impossible, we expect the ideas discussed in this paper to be relevant for experiments on many-body localization.

  • Figure
  • Received 4 March 2014
  • Revised 18 August 2014

DOI:https://doi.org/10.1103/PhysRevB.90.064203

©2014 American Physical Society

Authors & Affiliations

Rahul Nandkishore1, Sarang Gopalakrishnan2, and David A. Huse1,3

  • 1Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 3Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

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Issue

Vol. 90, Iss. 6 — 1 August 2014

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