Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class

Obuse H, Subramaniam AR, Furusaki A, Gruzberg IA, Ludwig AWW. Physical Review Letters, 98, 156802, 2007


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.