Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory.
We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition will have to satisfy. We find a nonparabolic multifractal spectrum and determine the ratio of boundary to bulk multifractal exponents. Our results rule out an exactly parabolic spectrum that has been the centerpiece in a number of proposals for critical field theories of the transition. In addition, we demonstrate analytically exact parabolicity of the related boundary spectra in the two-dimensional chiral orthogonal "Gade-Wegner" symmetry class.
Condensed Matter Theory Laboratory, RIKEN, Wako, Saitama 351-0198, Japan.
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Obuse
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Subramaniam
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Furusaki
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Gruzberg
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Ludwig