Fractal characteristics of critical and localized states in incommensurate quantum systems

Indubala I. Satija*, Jukka A. Ketoja

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Incommensurate quantum systems with two competing periodicities exhibit metallic (with Bloch-type extended wave functions), insulating (with exponentially localized wave functions) as well as critical (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.

Original languageEnglish
Pages (from-to)589-601
Number of pages13
JournalPramana: Journal of Physics
Volume48
Issue number2
DOIs
Publication statusPublished - 1 Jan 1997
MoE publication typeNot Eligible

Funding

The research of IIS is supported by a grant from National Science Foundation DMR 093296. IIS would like to acknowledge the hospitality of National Institue of Standard and Technology where part of this work was done. JAK would like to thank for the support by the Niilo Helander Foundation and for the hospitality during his visits to the George Mason University where this work was initiated.

Keywords

  • Fractal
  • Incommensurate systems
  • Localization

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