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

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    • 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

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      Posted on July 25, 2019

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