Fractal characteristics of critical and localized states in incommensurate quantum systems

Indubala I. Satija, Jukka A. Ketoja

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

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fractals
wave functions
electron gas
periodic variations
eigenvectors
envelopes
phase diagrams
scaling
magnetic fields

Keywords

  • Fractal
  • Incommensurate systems
  • Localization

Cite this

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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.",
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Fractal characteristics of critical and localized states in incommensurate quantum systems. / Satija, Indubala I.; Ketoja, Jukka A.

In: Pramana - Journal of Physics, Vol. 48, No. 2, 01.01.1997, p. 589-601.

Research output: Contribution to journalArticleScientificpeer-review

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