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

TL;DR

This paper investigates how boundary effects influence multifractal wave function scaling at the 2D spin quantum Hall transition, providing exact boundary exponents through supersymmetry and percolation mapping.

Contribution

It introduces exact boundary multifractal exponents for the spin quantum Hall transition using supersymmetry and percolation techniques, extending understanding of boundary criticality.

Findings

Exact boundary multifractal exponents derived

Mapping to classical percolation with reflecting boundaries

Analysis of boundary effects in various geometries

Abstract

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.