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Geometrical Description of the Fractional Quantum Hall Effect
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Geometrical Description of the Fractional Quantum Hall Effect
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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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Cited by 1 Pith paper
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Chiral Graviton Theory of Fractional Quantum Hall States
By gauging area-preserving diffeomorphisms and adding a Stueckelberg mass term, the paper constructs a nonlinear effective theory whose quadratic limit reproduces the bimetric description of the chiral spin-2 magnetoroton.
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