Critical behavior of the transport coefficients at the plateau-insulator transition in IQHE

Using the non-commutative Kubo formula for disordered lattice systems, we mapped the conductivity tensor $\sigma(E_F,T)$ as function of Fermi level $E_F$ and temperature T for the disordered Hofstadter model. Convergence and accuracy tests indicate that the simulations can be used to investigate the critical behavior near the plateau-insulator transition. Our analysis provides the first quantitative theoretical confirmation of the well established experimental facts about the critical behavior: 1) The semicircle law for the components of the conductivity tensor; 2) The existence of the quantized Hall insulator state characterized by zero direct and Hall conductivities, but with Hall resistivity quantized at $h/e^2$; 3) Single scaling behavior with exponents that are consistent with previous studies.