Dynamical critical behavior in the integer quantum Hall effect

We investigate dynamical scaling properties in the integer quantum Hall effect for non-interacting electrons at zero temperature, by means of the frequency-induced peak broadening of the dissipative longitudinal conductivity σ xx (ω). This quantity is calculated numerically in the lowest Landau level for various values of the Fermi energy E, of the frequency ω, and of the system size L. Data for the width W (ω, L) of the peak are analyzed by means of the dynamical finite-size scaling law W (ω, L) ≈ L −1/ν f (ωL z), where ν is the static critical exponent of the localization length, and z is the dynamical exponent. A fit of the data, assuming ν = 2.33 is known, yields z = 1.19 ± 0.13. This result indicates that the dynamical exponent in the integer quantum Hall effect may be different from the pertinent space dimension (d = 2), even in the absence of interactions between electrons.