Numerical-scaling experiments in Anderson localization

The Kubo-Greenwood formula is used to numerically evaluate the conductance for the Anderson model of three-dimensional noninteracting electrons in a uniformly distributed random potential. We construct the trajectory function {β}(g)=d lng/d lnL, verify that it depends on the single parameter g, and use it to calculate the critical exponent as {ν}=1.5±{}0.2. A new trajectory function is defined and evaluated that describes the scaling behavior of the renormalized ac conductivity. We numerically verify the ω1/3 frequency dependence of the ac conductivity.