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

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 $4\times 10^6$ 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.

arXiv comment11 pages, 8 figures. arXiv admin note: text overlap with arXiv:1107.5736

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