Critical parameters from a generalized multifractal analysis at the Anderson transition

Area of Science:

• Condensed matter physics
• Statistical physics

Background:

• Anderson localization describes the transition of electron wave functions from extended to localized states in disordered systems.
• Characterizing this transition often relies on transport measurements, which can be experimentally challenging.

Purpose of the Study:

• To develop a novel method for analyzing the Anderson localization-delocalization transition.
• To demonstrate that wave function amplitude distributions alone are sufficient to characterize the critical regime.
• To estimate critical parameters, including the critical exponent, without recourse to transport measurements.

Main Methods:

• Generalization of multifractal analysis applied to the critical regime.
• Analysis of the probability distribution of wave function amplitudes.
• Finite-size scaling combined with multifractal formalism.
• Exact diagonalization of the three-dimensional Anderson model.

Main Results:

• The probability distribution of wave function amplitudes effectively characterizes the Anderson transition.
• Critical parameters can be estimated solely from wave function statistics.
• The critical exponent ν was estimated as 1.58±0.03 for the 3D Anderson model.

Conclusions:

• A generalized multifractal analysis provides an effective route to study Anderson localization.
• This approach bypasses the need for transport measurements, simplifying critical parameter estimation.
• The findings offer new insights into the nature of the localization transition and its critical behavior.