The integer quantum Hall transition: an $S$-matrix approach to random networks

TL;DR

This paper introduces a new $S$-matrix method for simulating random network models of the integer quantum Hall transition, yielding critical exponents close to experimental values and improving upon previous transfer matrix techniques.

Contribution

The authors develop a novel $S$-matrix approach for network simulations, providing more accurate critical exponent estimates for the quantum Hall transition.

Findings

Critical exponent $ u \,\approx\, 2.4$ matches experimental data

Method outperforms transfer matrix approach

Results differ from Chalker-Coddington model predictions

Abstract

In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the Chalker-Coddington (CC) model for the integer quantum Hall transition that more faithfully capture the physics of electrons moving in a strong magnetic field and a smooth disorder potential. The new method has considerable advantages compared to the transfer matrix approach, and gives the value $\nu \approx 2.4$ 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 $\nu_{\text{exp}} \approx 2.38$ observed at the integer quantum Hall transition but substantially different from the CC value $\nu_\text{CC} \approx 2.6$.