Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition

TL;DR

This paper numerically investigates the multifractal exponents near the integer quantum Hall transition, confirming theoretical relations and accurately determining critical exponents while accounting for subleading corrections.

Contribution

The study introduces a numerical method to accurately determine multifractal exponents near the quantum Hall transition, overcoming challenges from subleading corrections.

Findings

Confirmed the relation between conductance and LDOS multifractal exponents.

Determined the leading irrelevant correction exponent y.

Provided independent numerical estimates for multifractal exponents.

Abstract

We study the critical behavior near the integer quantum Hall plateau transition by focusing on the multifractal (MF) exponents $X_q$ describing the scaling of the disorder-average moments of the point contact conductance $T$ between two points of the sample, within the Chalker-Coddington network model. Past analytical work has related the exponents $X_q$ to the MF exponents $\Delta_q$ of the local density of states (LDOS). To verify this relation, we numerically determine the exponents $X_q$ with high accuracy. We thereby provide, at the same time, independent numerical results for the MF exponents $\Delta_q$ for the LDOS. The presence of subleading corrections to scaling makes such determination directly from scaling of the moments of $T$ virtually impossible. We overcome this difficulty by using two recent advances. First, we construct pure scaling operators for the moments of $T$ which have precisely the same leading scaling behavior, but no subleading contributions. Secondly, we take into account corrections to scaling from irrelevant (in the renormalization group sense) scaling fields by employing a numerical technique ("stability map") recently developed by us. We thereby numerically confirm the relation between the two sets of exponents, $X_q$ (point contact conductances) and $\Delta_q$ (LDOS), and also determine the leading irrelevant (corrections to scaling) exponent $y$ as well as other subleading exponents. Our results suggest a way to access multifractality in an experimental setting.