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Updated: Dec 4, 2025
07:46
Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
8.8K
A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals.
Giovanni Antinucci1, Luca Fresta1, Marcello Porta2
1Institute of Mathematics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland.
Annales Henri Poincare
|October 22, 2020
Summary
We investigate disordered quantum systems using renormalization group methods and supersymmetry. Our findings demonstrate algebraic decay in correlation functions, indicating particle delocalization in these systems.
Area of Science:
- Condensed matter physics
- Quantum field theory
- Statistical mechanics
Background:
- Focuses on gapless, three-dimensional, weakly disordered quantum systems.
- These systems exhibit a pointlike Fermi surface and conical energy band intersections without disorder.
Purpose of the Study:
- To study a hierarchical supersymmetric model for these quantum systems.
- To compute correlation functions and analyze the impact of disorder.
Main Methods:
- Employs rigorous renormalization group (RG) methods.
- Utilizes supersymmetry to analyze the system's properties.
- Applies multiscale analysis of Gaussian integrations with imaginary covariances via stationary phase expansions.
Main Results:
- Proves algebraic decay of the two-point correlation function.
- Demonstrates that this decay is compatible with particle delocalization.
- Provides a rigorous framework for understanding disordered quantum systems.
Conclusions:
- The study establishes a theoretical model for disordered quantum systems with specific topological features.
- Confirms that weak disorder can lead to delocalization, a significant phenomenon in condensed matter physics.
- Highlights the power of supersymmetric and renormalization group techniques in tackling complex quantum problems.
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