Scaling and localization lengths of a topologically disordered system

Area of Science:

• Condensed matter physics
• Disordered systems
• Quantum mechanics

Background:

• Disordered systems are crucial for understanding phenomena like particle diffusion, glass relaxation, and semiconductor impurity bands.
• The Anderson model is a standard framework for studying electron localization in disordered materials.

Purpose of the Study:

• To investigate a noninteracting disordered system modeling particle diffusion, glass relaxation, and semiconductor impurity bands.
• To determine if this model exhibits universal behavior comparable to the standard Anderson model.
• To analyze the localization length as a function of energy and density.

Main Methods:

• Numerical simulations of a noninteracting disordered system.
• Finite-size scaling analysis to determine localization length.
• Examination of localized states beyond the delocalization transition.

Main Results:

• The model exhibits strong numerical evidence of universal behavior, mirroring the standard Anderson model.
• Localization length was successfully determined as a function of energy and density.
• Localized states were identified away from the delocalization transition.
• Results across various energies consistently fit a single universal scaling curve.

Conclusions:

• The noninteracting disordered system effectively models key physical phenomena.
• The model's universal behavior aligns with established theories like the Anderson model.
• Finite-size scaling provides a robust method for characterizing localization phenomena in disordered systems.