Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach

TL;DR

This paper develops a real-space renormalization group method for the quantum Hall effect transition, deriving a distribution of conductance and calculating critical exponents, with results compared to numerical simulations.

Contribution

It introduces a generalized RG approach for quantum percolation in the quantum Hall effect, providing analytical insights into conductance distribution and critical exponents.

Findings

Derived a closed RG equation for conductance distribution

Calculated the critical exponent of the localization length

Compared analytical results with numerical simulations

Abstract

We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.