• Fractal characteristics of critical and localized states in incommensurate quantum systems

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/048/02/0589-0601

    • Keywords

       

      Incommensurate systems; localization; fractal

    • Abstract

       

      Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well ascritical (with fractal wave functions) phases. An exact renormalization method, which takes into account the inherent incommensurability, is used to obtain the phase diagram of various quantum models for the two-dimensional electron gas and for quantum spin chains in a magnetic field. In this approach, the scaling properties of the fractal eigenstates are characterized by a fixed point or a strange invariant set of the renormalization flow. One of our novel results is the existence of self-similar fluctuations in the localized states once the exponentially decaying envelope is factorized out. In almost all cases under investigation here, the universality classes can be broadly classified as those of the nearest-neighbor square or triangular lattices.

    • Author Affiliations

       

      Indubala I Satija1 Jukka A Ketoja1 2

      1. Department of Physics and Institute of Computational Sciences and Informatics, George Mason University, Fairfax, VA - 22030, USA
      2. Department of Mathematics, University of Helsinki, P.O. Box 4 - FIN-00014, Finland
    • Dates

       
  • Pramana – Journal of Physics | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.