Integrated-conductance approach to scaling at the integer quantum Hall transition

We develop a method to study integer quantum Hall (IQH) criticality from finite size scaling of the energy-integrated conductance about the critical point. This method is inspired from the number of conducting states method of Bhatt and colleagues [Phys. Rev. B 99, 24205 (2019)] but (i) applies to non-Hamiltonian models including the Chalker Coddington (CC) network model and (ii) can access system sizes nearly two orders of magnitude larger than before.  Using this method, we find the localization length exponent ν ~ 2.6 for the CC network model, in agreement with the accepted literature value. We also confirm a substantially different value of ν for the two-layer analog of the CC network model, thought to be in the same universality class. This method may be useful for evaluating predictions from the conformal field theory recently proposed by M. Zirnbauer [Nucl. Phys. B 941, 458 (2019)] and for studying other Anderson transitions described by network models.