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

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

1999-11-30

arxiv.org/abs/cond-mat/9911476v1

Phys.Rev. B62 (2000) 15359-15362

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 1 figure, typeset in LaTeX (uses revtex)

Scientific paper

10.1103/PhysRevB.62.15359

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.

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