  The von Neumann entanglement entropy is a useful measure to characterize a
quantum phase transition. We investigate the non-analyticity of this entropy at
disorder-dominated quantum phase transitions in non-interacting electronic
systems. At these critical points, the von Neumann entropy is determined by the
single particle wave function intensity which exhibits complex scale invariant
fluctuations. We find that the concept of multifractality is naturally suited
for studying von Neumann entropy of the critical wave functions. Our numerical
simulations of the three dimensional Anderson localization transition and the
integer quantum Hall plateau transition show that the entanglement at these
transitions is well described using multifractal analysis.
