Scaling collapse of longitudinal conductance near the integer quantum Hall transition

Abstract

Within the mature field of Anderson transitions, the critical properties of the integer quantum Hall transition still pose a significant challenge. Numerical studies of the transition suffer from strong corrections to scaling for most observables. In this work, we suggest to overcome this problem by using the longitudinal conductance $g$ of the network model as the scaling observable, which we compute for system sizes nearly two orders of magnitude larger than in previous studies. We show numerically that the sizeable corrections to scaling of $g$ can be included in a remarkably simple form which leads to an excellent scaling collapse. Surprisingly, the scaling function turns out to be indistinguishable from a Gaussian. We propose a cost-function-based approach, and estimate $\nu =2.607(8)$, consistent with previous results, but considerably more precise than in most works on this problem. Extending previous approaches for Hamiltonian models, we also confirm our finding using integrated conductance as a scaling variable.

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• Integer Quantum Hall Effect: Disorder, temperature, floating, and plateau width
• Topological quantum criticality of the disordered Chern insulator
• The Case Against Smooth Null Infinity IV: Linearised Gravity Around Schwarzschild -- An Overview
• Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Irrelevant corrections at the quantum Hall transition
• Quantum Hall criticality in an amorphous Chern insulator
• Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum
• Emergent fractals in dirty topological crystals
• Coexistent multifractal mesoscopic fluctuations in Integer Quantum Hall Transition and in Orbital Hall Transition
• Nonequilibrium Critical Scaling of a Squeezing Phase Transition
• Random Magnetic Field and the Dirac Fermi Surface