---
_id: '834'
abstract:
- lang: eng
  text: 'Thermal and many-body localized phases are separated by a dynamical phase
    transition of a new kind. We analyze the distribution of off-diagonal matrix elements
    of local operators across this transition in two different models of disordered
    spin chains. We show that the behavior of matrix elements can be used to characterize
    the breakdown of thermalization and to extract the many-body Thouless energy.
    We find that upon increasing the disorder strength the system enters a critical
    region around the many-body localization transition. The properties of the system
    in this region are: (i) the Thouless energy becomes smaller than the level spacing,
    (ii) the matrix elements show critical dependence on the energy difference, and
    (iii) the matrix elements, viewed as amplitudes of a fictitious wave function,
    exhibit strong multifractality. This critical region decreases with the system
    size, which we interpret as evidence for a diverging correlation length at the
    many-body localization transition. Our findings show that the correlation length
    becomes larger than the accessible system sizes in a broad range of disorder strength
    values and shed light on the critical behavior near the many-body localization
    transition.'
acknowledgement: We   acknowledge   useful   discussions with V. Kravtsov, T. Grover,
  and R. Vasseur.  M.S. was supported by Gordon and Betty Moore Foundation’s EPiQS
  Initiative through Grant GBMF4307.  M.S. and D.A.  acknowledge  hospitality  of  KITP,  where  parts  of
  this work were completed (supported in part by the National Science Foundation under
  Grant No. NSF PHY11-25915)
article_number: '104201'
article_processing_charge: No
author:
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
- first_name: Papic
  full_name: Zlatko, Papic
  last_name: Zlatko
- first_name: Dmitry
  full_name: Abanin, Dmitry
  last_name: Abanin
citation:
  ama: Serbyn M, Zlatko P, Abanin D. Thouless energy and multifractality across the
    many-body localization transition. <i>Physical Review B - Condensed Matter and
    Materials Physics</i>. 2017;96(10). doi:<a href="https://doi.org/10.1103/PhysRevB.96.104201">10.1103/PhysRevB.96.104201</a>
  apa: Serbyn, M., Zlatko, P., &#38; Abanin, D. (2017). Thouless energy and multifractality
    across the many-body localization transition. <i>Physical Review B - Condensed
    Matter and Materials Physics</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevB.96.104201">https://doi.org/10.1103/PhysRevB.96.104201</a>
  chicago: Serbyn, Maksym, Papic Zlatko, and Dmitry Abanin. “Thouless Energy and Multifractality
    across the Many-Body Localization Transition.” <i>Physical Review B - Condensed
    Matter and Materials Physics</i>. American Physical Society, 2017. <a href="https://doi.org/10.1103/PhysRevB.96.104201">https://doi.org/10.1103/PhysRevB.96.104201</a>.
  ieee: M. Serbyn, P. Zlatko, and D. Abanin, “Thouless energy and multifractality
    across the many-body localization transition,” <i>Physical Review B - Condensed
    Matter and Materials Physics</i>, vol. 96, no. 10. American Physical Society,
    2017.
  ista: Serbyn M, Zlatko P, Abanin D. 2017. Thouless energy and multifractality across
    the many-body localization transition. Physical Review B - Condensed Matter and
    Materials Physics. 96(10), 104201.
  mla: Serbyn, Maksym, et al. “Thouless Energy and Multifractality across the Many-Body
    Localization Transition.” <i>Physical Review B - Condensed Matter and Materials
    Physics</i>, vol. 96, no. 10, 104201, American Physical Society, 2017, doi:<a
    href="https://doi.org/10.1103/PhysRevB.96.104201">10.1103/PhysRevB.96.104201</a>.
  short: M. Serbyn, P. Zlatko, D. Abanin, Physical Review B - Condensed Matter and
    Materials Physics 96 (2017).
date_created: 2018-12-11T11:48:45Z
date_published: 2017-09-06T00:00:00Z
date_updated: 2023-09-26T15:51:54Z
day: '06'
department:
- _id: MaSe
doi: 10.1103/PhysRevB.96.104201
external_id:
  isi:
  - '000409429300004'
intvolume: '        96'
isi: 1
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1610.02389
month: '09'
oa: 1
oa_version: Submitted Version
publication: Physical Review B - Condensed Matter and Materials Physics
publication_identifier:
  issn:
  - '24699950'
publication_status: published
publisher: American Physical Society
publist_id: '6814'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thouless energy and multifractality across the many-body localization transition
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 96
year: '2017'
...
---
_id: '724'
abstract:
- lang: eng
  text: We investigate the stationary and dynamical behavior of an Anderson localized
    chain coupled to a single central bound state. Although this coupling partially
    dilutes the Anderson localized peaks towards nearly resonant sites, the most weight
    of the original peaks remains unchanged. This leads to multifractal wave functions
    with a frozen spectrum of fractal dimensions, which is characteristic for localized
    phases in models with power-law hopping. Using a perturbative approach we identify
    two different dynamical regimes. At weak couplings to the central site, the transport
    of particles and information is logarithmic in time, a feature usually attributed
    to many-body localization. We connect such transport to the persistence of the
    Poisson statistics of level spacings in parts of the spectrum. In contrast, at
    stronger couplings the level repulsion is established in the entire spectrum,
    the problem can be mapped to the Fano resonance, and the transport is ballistic.
acknowledgement: "We  would  like  to  thank  Dmitry  Abanin,  Christophe  De\r\nBeule,
  \ Joel  Moore,  Romain  Vasseur,  and  Norman  Yao  for\r\nmany  stimulating  discussions.
  \ Financial  support  has  been\r\nprovided  by  the  Deutsche  Forschungsgemeinschaft
  \ (DFG)\r\nvia Grant No. TR950/8-1, SFB 1170 “ToCoTronics” and the\r\nENB  Graduate
  \ School  on  Topological  Insulators.  M.S.  was\r\nsupported by Gordon and Betty
  Moore Foundation’s EPiQS\r\nInitiative through Grant No. GBMF4307. F.P. acknowledges\r\nsupport
  from the DFG Research Unit FOR 1807 through Grant\r\nNo. PO 1370/2-1."
article_number: '104203'
author:
- first_name: Daniel
  full_name: Hetterich, Daniel
  last_name: Hetterich
- first_name: Maksym
  full_name: Serbyn, Maksym
  id: 47809E7E-F248-11E8-B48F-1D18A9856A87
  last_name: Serbyn
  orcid: 0000-0002-2399-5827
- first_name: Fernando
  full_name: Domínguez, Fernando
  last_name: Domínguez
- first_name: Frank
  full_name: Pollmann, Frank
  last_name: Pollmann
- first_name: Björn
  full_name: Trauzettel, Björn
  last_name: Trauzettel
citation:
  ama: Hetterich D, Serbyn M, Domínguez F, Pollmann F, Trauzettel B. Noninteracting
    central site model localization and logarithmic entanglement growth. <i>Physical
    Review B</i>. 2017;96(10). doi:<a href="https://doi.org/10.1103/PhysRevB.96.104203">10.1103/PhysRevB.96.104203</a>
  apa: Hetterich, D., Serbyn, M., Domínguez, F., Pollmann, F., &#38; Trauzettel, B.
    (2017). Noninteracting central site model localization and logarithmic entanglement
    growth. <i>Physical Review B</i>. American Physical Society. <a href="https://doi.org/10.1103/PhysRevB.96.104203">https://doi.org/10.1103/PhysRevB.96.104203</a>
  chicago: Hetterich, Daniel, Maksym Serbyn, Fernando Domínguez, Frank Pollmann, and
    Björn Trauzettel. “Noninteracting Central Site Model Localization and Logarithmic
    Entanglement Growth.” <i>Physical Review B</i>. American Physical Society, 2017.
    <a href="https://doi.org/10.1103/PhysRevB.96.104203">https://doi.org/10.1103/PhysRevB.96.104203</a>.
  ieee: D. Hetterich, M. Serbyn, F. Domínguez, F. Pollmann, and B. Trauzettel, “Noninteracting
    central site model localization and logarithmic entanglement growth,” <i>Physical
    Review B</i>, vol. 96, no. 10. American Physical Society, 2017.
  ista: Hetterich D, Serbyn M, Domínguez F, Pollmann F, Trauzettel B. 2017. Noninteracting
    central site model localization and logarithmic entanglement growth. Physical
    Review B. 96(10), 104203.
  mla: Hetterich, Daniel, et al. “Noninteracting Central Site Model Localization and
    Logarithmic Entanglement Growth.” <i>Physical Review B</i>, vol. 96, no. 10, 104203,
    American Physical Society, 2017, doi:<a href="https://doi.org/10.1103/PhysRevB.96.104203">10.1103/PhysRevB.96.104203</a>.
  short: D. Hetterich, M. Serbyn, F. Domínguez, F. Pollmann, B. Trauzettel, Physical
    Review B 96 (2017).
date_created: 2018-12-11T11:48:09Z
date_published: 2017-09-13T00:00:00Z
date_updated: 2021-01-12T08:12:35Z
day: '13'
department:
- _id: MaSe
doi: 10.1103/PhysRevB.96.104203
intvolume: '        96'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1701.02744
month: '09'
oa: 1
oa_version: Submitted Version
publication: Physical Review B
publication_identifier:
  issn:
  - '24699950'
publication_status: published
publisher: American Physical Society
publist_id: '6955'
quality_controlled: '1'
scopus_import: 1
status: public
title: Noninteracting central site model localization and logarithmic entanglement
  growth
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 96
year: '2017'
...