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# Multifractal finite-size scaling at the Anderson transition in the unitary symmetry class

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### Abstract

We use multifractal finite-size scaling to perform a high-precision numerical study of the critical properties of the Anderson localization-delocalization transition in the unitary symmetry class, considering the Anderson model including a random magnetic flux. We demonstrate the scale invariance of the distribution of wavefunction intensities at the critical point and study its behavior across the transition. Our analysis, involving more than $$4\times10^6$$ independently generated wavefunctions of system sizes up to $$L^3=150^3$$, yields accurate estimates for the critical exponent of the localization length, $$\nu=1.446 (1.440,1.452)$$, the critical value of the disorder strength and the multifractal exponents.

### Most cited references38

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### Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

(1979)
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### Disordered electronic systems

(1985)
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### Anderson Transitions

(2007)
The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.
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### Author and article information

###### Journal
17 July 2017
###### Article
1707.05701