Numerical evidence for marginal scaling at the integer quantum Hall transition

The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling flow close to the critical point in the parameter plane spanned by longitudinal and transversal conductivity has been studied vigorously both in experiment and numerical simulations. Despite all efforts, the IQHT is notoriously difficult for pinning down the precise value of critical exponents, which seem to vary with model details, challenging the principle of universality. Recently, M. Zirnbauer [Nucl. Phys. B 941, 458 (2019)] has conjectured a conformal field theory for the transition, in which the fixed point is exactly marginal, leading
to a very slow scaling flow in its vicinity. In this work, we provide numerical evidence for such a scenario by using extensive simulations of various incarnations of network models at unprecedented length scales. At criticality, we confirm the marginal scaling of the longitudinal conductivity towards the fixed-point value σ^*=2/π. Away from criticality we describe a mechanism that could account for the emergence of an effective localization length exponent ν_eff, which is necessarily model dependent. We confirm this idea by exact numerical determination of ν_eff in suitably chosen models.