Derivation of the semicircle law from the law of corresponding states
Abstract
We show that, for the transition between any two quantum Hall states, the semicircle 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 favors taking the two-dimensional flow seriously for the whole transition, and not just near the critical points.
- Publication:
-
Physical Review B
- Pub Date:
- December 2000
- DOI:
- 10.1103/PhysRevB.62.15359
- arXiv:
- arXiv:cond-mat/9911476
- Bibcode:
- 2000PhRvB..6215359B
- Keywords:
-
- 73.40.Hm;
- 05.30.Fk;
- 02.20.-a;
- Fermion systems and electron gas;
- Group theory;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- High Energy Physics - Theory
- E-Print:
- 4 pages, 1 figure, typeset in LaTeX (uses revtex)