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Multifractal scaling of critical wave functions at a disorder-driven(Anderson) localization transition is modified near boundaries of a sample.Here this effect is studied for the example of the spin quantum Hall plateautransition using the supersymmetry technique for disorder averaging. Uponmapping of the spin quantum Hall transition to the classical percolationproblem with reflecting boundaries, a number of multifractal exponentsgoverning wave function scaling near a boundary are obtained exactly. Moreover,additional exact boundary scaling exponents of the localization problem areextracted, and the problem is analyzed in other geometries.

Boundary criticality and multifractality at the 2D spin quantum Hall transition