Mobility edges in one-dimensional models with quasi-periodic disorder

Area of Science:

• Condensed matter physics
• Quantum mechanics
• Disordered systems

Background:

• One-dimensional tight binding models are crucial for understanding electron behavior.
• Quasi-periodic disorders introduce complex localization phenomena.
• Mobility edges delineate extended and localized states in energy spectra.

Purpose of the Study:

• To develop an efficient method for determining mobility edges in quasi-periodic disordered models.
• To approximate complex disordered systems using an ensemble of periodic models.
• To propose a new index for quantifying eigenstate localization.

Main Methods:

• Approximating quasi-periodic disordered models with an ensemble of periodic models.
• Determining mobility edges via the overlaps of energy bands from these periodic models.
• Developing a localization index based on the approximate method.

Main Results:

• The approximate method accurately determines the precise location of mobility edges.
• The overlap of energy bands effectively predicts mobility edges.
• A novel index quantifies the degree of localization for each eigenstate.

Conclusions:

• The proposed method offers an efficient and accurate way to study mobility edges in quasi-periodic disordered systems.
• This approach simplifies the analysis of complex quantum phenomena.
• The localization index provides a valuable tool for characterizing electronic states.