RESUMO
Critical properties of quantum Hall systems are affected by the presence of extra edge channels-those that are present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using supersymmetry, we map the corresponding network model to a classical loop model, whose boundary critical behavior was recently determined exactly. We verify predictions of the exact solution by extensive numerical simulations.
RESUMO
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.
RESUMO
We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.
