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

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.