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Updated: May 4, 2026
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Published on: January 28, 2021
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Calculation of multi-fractal dimensions in spin chains
1Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), , UMR 8626, CNRS, Université Paris-Sud, 15 rue Georges Clémenceau, 91405 Orsay, France.
Summary
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.
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.
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