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arXiv · hep-th/9211071

Conformal Symmetry and Universal Properties of Quantum Hall States

A. Cappelli·G. V. Dunne·C. A. Trugenberger·G. R. Zemba
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Abstract

The low-lying excitations of a quantum Hall state on a disk geometry are edge excitations. Their dynamics is governed by a conformal field theory on the cylinder defined by the disk boundary and the time variable. We give a simple and detailed derivation of this conformal field theory for integer filling, starting from the microscopic dynamics of $(2+1)$-dimensional non-relativistic electrons in Landau levels. This construction can be generalized to describe Laughlin's fractional Hall states via chiral bosonization, thereby making contact with the effective Chern-Simons theory approach. The conformal field theory dictates the finite-size effects in the energy spectrum. An experimental or numerical verification of these universal effects would provide a further confirmation of Laughlin's theory of incompressible quantum fluids.

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A. Cappelli, G. V. Dunne, C. A. Trugenberger, G. R. Zemba. 1992-11-16. Conformal Symmetry and Universal Properties of Quantum Hall States. https://doi.org/10.1016/0550-3213(93)90603-m

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