Geometrical description of the fractional quantum Hall effect.

  title={Geometrical description of the fractional quantum Hall effect.},
  author={F. D. M. Haldane},
  journal={Physical review letters},
  volume={107 11},
  • F. Haldane
  • Published 17 June 2011
  • Physics, Medicine
  • Physical review letters
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. 

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