Geometrically Disordered Network Models for the Integer Quantum Hall Transition via Loop Diagram Insertion

In [1], the transfer matrix method for the Chalker-Coddington (CC) Network Model of the Integer Quantum Hall transition was used on a lattice with random node removal to compute the localization critical exponent ν. We introduce a new method for including topological disorder in the lattice for the CC Network Model by randomly replacing nodes in the square lattice with diagrams including closed loops for which the transfer matrices can be explicitly computed. We then numerically compute ν for a variety of widths and random edge phases, and thus determine the characteristic localization length for electrons on the sample. By varying the node replacement probability, we also evaluate the effects of different levels of disorder on the value obtained for the localization exponent. 

[1] I. A. Gruzberg, A. Klu ̈mper, W. Nuding, and A. Sedrakyan. Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum hall plateau transitions. Phys. Rev. B, 95:125414, Mar 2017.