Algebraic localization from power-law couplings in disordered quantum wires

Thomas Botzung, Davide Vodola, Piero Naldesi, Markus Müller, Elisa Ercolessi, and Guido Pupillo
Phys. Rev. B 100, 155136 – Published 22 October 2019

Abstract

We analyze the effects of disorder on the correlation functions of one-dimensional quantum models of fermions and spins with long-range interactions that decay with distance as a power law 1/α. Using a combination of analytical and numerical results, we demonstrate that power-law interactions imply a long-distance algebraic decay of correlations within disordered-localized phases, for all exponents α. The exponent of algebraic decay depends only on α, and not, e.g., on the strength of disorder. We find a similar algebraic localization for wave functions. These results are in contrast to expectations from short-range models and are of direct relevance for a variety of quantum mechanical systems in atomic, molecular, and solid-state physics.

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  • Received 24 October 2018
  • Revised 13 September 2019

DOI:https://doi.org/10.1103/PhysRevB.100.155136

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Thomas Botzung1,2, Davide Vodola3,*, Piero Naldesi4,5, Markus Müller3, Elisa Ercolessi2,6, and Guido Pupillo1,†

  • 1University of Strasbourg, CNRS, ISIS (UMR 7006) and IPCMS (UMR 7504), 67000 Strasbourg, France
  • 2Dipartimento di Fisica e Astronomia dell'Università di Bologna, I-40127 Bologna, Italy
  • 3Department of Physics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom
  • 4Université Grenoble-Alpes, LPMMC, F-38000 Grenoble, France
  • 5CNRS, LPMMC, F-38000 Grenoble, France
  • 6INFN, Sezione di Bologna, I-40127 Bologna, Italy

  • *davide.vodola@gmail.com
  • pupillo@unistra.fr

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Issue

Vol. 100, Iss. 15 — 15 October 2019

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