Duality in Power-Law Localization in Disordered One-Dimensional Systems

verfasst von: X. Deng, V. E. Kravtsov, G. V. Shlyapnikov, L. Santos
Abstract: The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1/ra. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of a>0. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops (a<1) and short-range hops (a>1), in which the wave function amplitude falls off algebraically with the same power γ from the localization center.
Organisationseinheit(en): Institut für Theoretische Physik
SFB 1227: Designte Quantenzustände der Materie (DQ-mat)
Externe Organisation(en): Abdus Salam International Centre for Theoretical Physics
Landau Institute for Theoretical Physics
Universite Paris-Sud
Universität Paris-Saclay
National University of Science and Technology MISIS
Universiteit van Amsterdam (UvA)
Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences
Typ: Artikel
Journal: Physical Review Letters
Band: 120
ISSN: 0031-9007
Publikationsdatum: 16.03.2018
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Physik und Astronomie (insg.)
Elektronische Version(en): https://doi.org/10.48550/arXiv.1706.04088 (Zugang: Offen)
https://doi.org/10.1103/PhysRevLett.120.110602 (Zugang: Geschlossen)
https://dare.uva.nl/personal/pure/en/publications/duality-in-powerlaw-localization-in-disordered-onedimensional-systems(ae666e42-87ba-4a21-bc48-969ec6a36e10).html (Zugang: Offen)

BibTeX

@article{523323e907594982a100bb423a842d3c,
title = "Duality in Power-Law Localization in Disordered One-Dimensional Systems",
abstract = "The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1/ra. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of a>0. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops (a<1) and short-range hops (a>1), in which the wave function amplitude falls off algebraically with the same power γ from the localization center.",
author = "X. Deng and Kravtsov, {V. E.} and Shlyapnikov, {G. V.} and L. Santos",
note = "Funding information: We acknowledge fruitful discussions with B. L. Altshuler, I. Khaymovich, and E. Yuzbashyan. X. D. and L. S. thank the support of the DFG (SFB 1227 DQ-mat and FOR2247). G. V. S. acknowledges funding from the European Research Council under European Community{\textquoteright}s Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 341197).",
year = "2018",
month = mar,
day = "16",
doi = "10.48550/arXiv.1706.04088",
language = "English",
volume = "120",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "11",
}