Fractal characteristics of critical and localized states in incommensurate quantum systems

Indubala I. Satija, Jukka A. Ketoja

Research output: Contribution to journalArticleScientificpeer-review


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
Issue number2
Publication statusPublished - 1 Jan 1997
MoE publication typeNot Eligible


  • Fractal
  • Incommensurate systems
  • Localization


Dive into the research topics of 'Fractal characteristics of critical and localized states in incommensurate quantum systems'. Together they form a unique fingerprint.

Cite this