Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class

H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, A. W. W. Ludwig

Published 2006-09-07, updated 2007-04-13Version 2

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.