Integer quantum Hall transition: An S -matrix approach to random networks

Abstract

In this paper we propose an S-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work [I. A. Gruzberg, A. Klümper, W. Nuding, and A. Sedrakyan, Phys. Rev. B 95, 125414 (2017)2469-995010.1103/PhysRevB.95.125414]. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully captures the physics of electrons moving in a strong magnetic field and a smooth disorder potential. This method has considerable advantages compared to the transfer matrix approach and gives the value ν≈2.4 for the critical exponent of the localization length in a random network. This finding confirms our previous result and is surprisingly close to the experimental value νexpt≈2.38 observed at the integer quantum Hall transition but substantially different from the CC value νCC≈2.6.