Derivation of the Semi-circle Law from the Law of Corresponding States

TL;DR

This paper derives the semi-circle law and duality symmetry in quantum Hall transitions from the law of corresponding states, establishing their exactness at zero temperature and emphasizing the importance of two-dimensional flow in experiments.

Contribution

It provides a theoretical derivation of the semi-circle law and duality symmetry from the law of corresponding states, clarifying their fundamental nature in quantum Hall transitions.

Findings

Semi-circle law and duality symmetry follow from the law of corresponding states.

These effects are exact at zero temperature, independent of microscopic details.

Experimental evidence supports the significance of two-dimensional flow throughout the transition.

Abstract

We show that, for the transition between any two quantum Hall states, the semi-circle law and the existence of a duality symmetry follow solely from the consistency of the law of corresponding states with the two-dimensional scaling flow. This puts these two effects on a sound theoretical footing, implying that both should hold exactly at zero temperature, independently of the details of the microscopic electron dynamics. This derivation also shows how the experimental evidence favours taking the two-dimensional flow seriously for the whole transition, and not just near the critical points.