Infinite symmetry in the quantum Hall effect
Abstract
Free planar electrons in a uniform magnetic field are shown to possess the dynamical symmetry of areapreserving diffeomorphisms (Winfinity algebra). Intuitively, this is a consequence of gauge invariance, which forces dynamics to depend only on the flux. The infinity of generators of this symmetry act within each Landau level, which is infinite dimensional in the thermodynamic limit. The incompressible ground states corresponding to completely filled Landau levels (integer quantum Hall effect) possess a dynamical symmetry, since they are left invariant by an infinite subset of generators. This geometrical characterization of incompressibility also holds for fractional fillings of the lowest level (simplest fractional Hall effect) in the presence of Haldane's effective twobody interactions. Although these modify the symmetry algebra, the corresponding incompressible ground states proposed by Laughlin are again symmetric with respect to the modified infinite algebra.
 Publication:

Nuclear Physics B
 Pub Date:
 May 1993
 DOI:
 10.1016/05503213(93)90660H
 arXiv:
 arXiv:hepth/9206027
 Bibcode:
 1993NuPhB.396..465C
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 28 pages