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Calculation of multi-fractal dimensions in spin chains.

Y Y Atas1, E Bogomolny

  • 1Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), , UMR 8626, CNRS, Université Paris-Sud, 15 rue Georges Clémenceau, 91405 Orsay, France.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 18, 2013
PubMed
Summary
This summary is machine-generated.

Ground-state wave functions in one-dimensional spin models exhibit multifractal properties. This study provides detailed analytical derivations and numerical evidence to confirm this finding in the natural spin-z basis.

Keywords:
ground-state wave functionmulti-fractalityspin chains

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Statistical physics

Background:

  • Previous research indicated multifractal characteristics in ground-state wave functions of certain one-dimensional spin models.
  • The natural spin-z basis is crucial for analyzing these wave functions.

Purpose of the Study:

  • To provide detailed analytical derivations supporting the multifractal nature of ground-state wave functions.
  • To present numerical confirmations of these multifractal properties.
  • To expand on the findings of Atas & Bogomolny (2012).

Main Methods:

  • Analytical derivation techniques applied to one-dimensional spin models.
  • Numerical simulations and calculations to verify theoretical predictions.
  • Analysis of wave functions in the natural spin-z basis.

Main Results:

  • Confirmed that ground-state wave functions for a wide range of one-dimensional spin models are multifractals.
  • Detailed analytical proofs were established for the multifractal nature.
  • Numerical results consistently supported the theoretical findings.

Conclusions:

  • The multifractal nature of ground-state wave functions in these models is robust.
  • The findings have implications for understanding quantum systems and complex wave function behavior.
  • This work solidifies the understanding of multifractality in condensed matter systems.