Geometrical Description of the Fractional Quantum Hall Effect

Abstract

The fundamental collective degree of freedom of fractional quantum Hall states is identified as a unimodular two-dimensional spatial metric that characterizes the local shape of the correlations of the incompressible fluid. Its quantum fluctuations are controlled by a topologically-quantized "guiding-center spin". Charge fluctuations are proportional to its Gaussian curvature.

4 pages, 0 figures; typo in formula for gaussian curvature of quasiparticle (p 4, last paragraph) fixed

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