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

• Main Authors: Subramaniam, Arvind R, Gruzberg, Ilya A, Ludwig, Andreas W. W
• Format: Journal Article
• Language: English
• Published: 07-12-2008
• Subjects: Physics - Mesoscale and Nanoscale Physics; Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.0803.1343

Phys. Rev. B 78, 245105 (2008) 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 plateau
transition using the supersymmetry technique for disorder averaging. Upon
mapping of the spin quantum Hall transition to the classical percolation
problem with reflecting boundaries, a number of multifractal exponents
governing wave function scaling near a boundary are obtained exactly. Moreover,
additional exact boundary scaling exponents of the localization problem are
extracted, and the problem is analyzed in other geometries.