  We study the time evolution of quenched random-mass Dirac fermions in one
dimension by quantum lattice Boltzmann simulations. For nonzero noise strength,
the diffusion of an initial wave packet stops after a finite time interval,
reminiscent of Anderson localization. However, instead of exponential
localization we find algebraically decaying tails in the disorder-averaged
density distribution. These qualitatively match $\propto x^{-3/2}$ decay, which
has been predicted by analytic calculations based on zero-energy solutions of
the Dirac equation.
