Nonperturbative Renormalization Group Function for Quantum Hall Plateau Transitions Imposed by Global Symmetries

Details Nonperturbative Renormalization Group Function for Quantum Hall Plateau Transitions Imposed by Global Symmetries Nonperturbative Renormalization Group Function for Quantum Hall Plateau Transitions Imposed by Global Symmetries

1998-10-26

arxiv.org/abs/cond-mat/9810334v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, REVTeX + multicol.sty

Scientific paper

As a unified theory of integer and fractional quantum Hall plateau transitions, a nonperturbative theory of the two-parameter scaling renormalization group function is presented. By imposing global symmetries known as ``the law of corresponding states'', we seek a possible form of renormalization group flows. Asking for consistency with the result from weak-localization perturbation theory, such restriction is so intense that we can analytically determine its concrete form. Accordingly, the critical exponent $\nu$ and the irrelevant scaling index $y$ are obtained analytically and turn out to be irrational. Their values ($\nu\approx 2.1$, $y\approx 0.3$) agree favorably well with experiments and numerics.

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