Large N Limit in the Quantum Hall Effect

Details Large N Limit in the Quantum Hall Effect Large N Limit in the Quantum Hall Effect

1993-03-04

arxiv.org/abs/hep-th/9303030v1

Phys.Lett.B306:100-107,1993

Physics

High Energy Physics

High Energy Physics - Theory

13 pages (+1 figure, available upon request), CERN-TH 6810/93

Scientific paper

10.1016/0370-2693(93)91144-C

The Laughlin states for $N$ interacting electrons at the plateaus of the fractional Hall effect are studied in the thermodynamic limit of large $N$. It is shown that this limit leads to the semiclassical regime for these states, thereby relating their stability to their semiclassical nature. The equivalent problem of two-dimensional plasmas is solved analytically, to leading order for $N\to\infty$, by the saddle point approximation - a two-dimensional extension of the method used in random matrix models of quantum gravity and gauge theories. To leading order, the Laughlin states describe classical droplets of fluids with uniform density and sharp boundaries, as expected from the Laughlin ``plasma analogy''. In this limit, the dynamical $W_\infty$-symmetry of the quantum Hall states expresses the kinematics of the area-preserving deformations of incompressible liquid droplets.

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