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 non-parabolic multifractal spectrum and we further 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 related boundary spectra in the 2D chiral orthogonal `Gade-Wegner' symmetry class. 
H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, A. W. W.   Ludwig