---
_id: '445'
abstract:
- lang: eng
  text: The Loschmidt echo, defined as the overlap between quantum wave function evolved
    with different Hamiltonians, quantifies the sensitivity of quantum dynamics to
    perturbations and is often used as a probe of quantum chaos. In this work we consider
    the behavior of the Loschmidt echo in the many-body localized phase, which is
    characterized by emergent local integrals of motion and provides a generic example
    of nonergodic dynamics. We demonstrate that the fluctuations of the Loschmidt
    echo decay as a power law in time in the many-body localized phase, in contrast
    to the exponential decay in few-body ergodic systems. We consider the spin-echo
    generalization of the Loschmidt echo and argue that the corresponding correlation
    function saturates to a finite value in localized systems. Slow, power-law decay
    of fluctuations of such spin-echo-type overlap is related to the operator spreading
    and is present only in the many-body localized phase, but not in a noninteracting
    Anderson insulator. While most of the previously considered probes of dephasing
    dynamics could be understood by approximating physical spin operators with local
    integrals of motion, the Loschmidt echo and its generalizations crucially depend
    on the full expansion of the physical operators via local integrals of motion
    operators, as well as operators which flip local integrals of motion. Hence these
    probes allow one to get insights into the relation between physical operators
    and local integrals of motion and access the operator spreading in the many-body
    localized phase.
acknowledgement: "This research was supported in part by the National\r\nScience Foundation
  under Grant No. NSF PHY11-25915.\r\nM.S. was supported by Gordon and Betty Moore
  Foundation’s\r\nEPiQS Initiative through Grant No. GBMF4307. D.A. also\r\nacknowledges
  support by Swiss National Science Foundation."
article_processing_charge: No
arxiv: 1
author:
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
- first_name: Dimitry
  full_name: Abanin, Dimitry
  last_name: Abanin
citation:
  ama: Serbyn M, Abanin D. Loschmidt echo in many body localized phases. <i>Physical
    Review B - Condensed Matter and Materials Physics</i>. 2017;96(1). doi:<a href="https://doi.org/10.1103/PhysRevB.96.014202">10.1103/PhysRevB.96.014202</a>
  apa: Serbyn, M., &#38; Abanin, D. (2017). Loschmidt echo in many body localized
    phases. <i>Physical Review B - Condensed Matter and Materials Physics</i>. American
    Physical Society. <a href="https://doi.org/10.1103/PhysRevB.96.014202">https://doi.org/10.1103/PhysRevB.96.014202</a>
  chicago: Serbyn, Maksym, and Dimitry Abanin. “Loschmidt Echo in Many Body Localized
    Phases.” <i>Physical Review B - Condensed Matter and Materials Physics</i>. American
    Physical Society, 2017. <a href="https://doi.org/10.1103/PhysRevB.96.014202">https://doi.org/10.1103/PhysRevB.96.014202</a>.
  ieee: M. Serbyn and D. Abanin, “Loschmidt echo in many body localized phases,” <i>Physical
    Review B - Condensed Matter and Materials Physics</i>, vol. 96, no. 1. American
    Physical Society, 2017.
  ista: Serbyn M, Abanin D. 2017. Loschmidt echo in many body localized phases. Physical
    Review B - Condensed Matter and Materials Physics. 96(1).
  mla: Serbyn, Maksym, and Dimitry Abanin. “Loschmidt Echo in Many Body Localized
    Phases.” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol.
    96, no. 1, American Physical Society, 2017, doi:<a href="https://doi.org/10.1103/PhysRevB.96.014202">10.1103/PhysRevB.96.014202</a>.
  short: M. Serbyn, D. Abanin, Physical Review B - Condensed Matter and Materials
    Physics 96 (2017).
date_created: 2018-12-11T11:46:31Z
date_published: 2017-07-12T00:00:00Z
date_updated: 2025-09-04T06:59:31Z
day: '12'
doi: 10.1103/PhysRevB.96.014202
extern: '1'
external_id:
  arxiv:
  - '1701.07772'
intvolume: '        96'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1701.07772
month: '07'
oa: 1
oa_version: Preprint
publication: Physical Review B - Condensed Matter and Materials Physics
publication_status: published
publisher: American Physical Society
publist_id: '7378'
status: public
title: Loschmidt echo in many body localized phases
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 96
year: '2017'
...