On the Implications of Discrete Symmetries for the Beta Function of Quantum Hall Systems

Details On the Implications of Discrete Symmetries for the Beta Function of Quantum Hall Systems On the Implications of Discrete Symmetries for the Beta Function of Quantum Hall Systems

1998-12-24

arxiv.org/abs/cond-mat/9812396v2

Phys.Lett. B451 (1999) 365-371

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Minor typographical errors corrected. 6 pages, LaTeX, no figures

Scientific paper

We argue that the large discrete symmetry group of quantum Hall systems is insufficient in itself to determine the complete beta function for the scaling of the conductivities, $\sigma_{xx}$ and $\sigma_{xy}$. We illustrate this point by showing that a recent ansatz for this function is one of a many-parameter family. A clean prediction for the delocalization exponents for these systems therefore requires the specification of more information, such as past proposals that the beta function is either holomorphic or quasi-holomorphic in the variable $z = (\hbar/e^2)(\sigma_{xy} + i\sigma_{xx})$.

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