Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory

Obuse H, Subramaniam AR, Furusaki A, Gruzberg IA, Ludwig AWW. Physical Review Letters, 101, 116802, 2008


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.