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

authored by

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.

Organisation(s)

Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)

External Organisation(s)

Abdus Salam International Centre for Theoretical Physics
Landau Institute for Theoretical Physics
Universite Paris-Sud
Université Paris-Saclay
National University of Science and Technology MISIS
University of Amsterdam
Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences

Type

Article

Journal

Physical Review Letters

Volume

120

ISSN

0031-9007

Publication date

16.03.2018

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Physics and Astronomy(all)

Electronic version(s)

https://doi.org/10.48550/arXiv.1706.04088 (Access: Open)
https://doi.org/10.1103/PhysRevLett.120.110602 (Access: Closed)
https://dare.uva.nl/personal/pure/en/publications/duality-in-powerlaw-localization-in-disordered-onedimensional-systems(ae666e42-87ba-4a21-bc48-969ec6a36e10).html (Access: Open)