STRUCTURING THE SET OF INCOMPRESSIBLE QUANTUM HALL FLUIDS

Abstract

A classification of incompressible quantum Hall fluids in terms of integral lattices and arithmetical invariants thereof is proposed. This classification enables us to characterize the plateau values of the Hall conductivity $\sH$ in the interval $(0,1]$ (in units where $e^2/h=1$) corresponding to ``stable'' incompressible quantum Hall fluids. A bijection, called shift map, between classes of stable incompressible quantum Hall fluids corresponding to plateaux of $\sH$ in the intervals $\,[1/(2\mini p+1),1/(2\mini p-1)\mini)\,$ and $\,[1/(2\mini q+1),1/(2\mini q-1)\mini)$, respectively, is constructed, with $p,q=1,2,3,(\dots ),p\ne q$. Our theoretical results are carefully compared to experimental data, and various predictions and experimental implications of our theory are discussed.

40 pages, LaTeX, 1 figure included; (for some possible macro issues, see the remarks about ``ways of producing the symbols for number fields'' in the preamble)

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