Exact exponents for the spin quantum Hall transition
Ilya A. Gruzberg, Andreas W. W. Ludwig, and N. Read
TL;DR
This paper derives exact critical exponents for the spin quantum Hall transition by mapping it onto a percolation problem using supersymmetry, providing precise results that align with numerical data.
Contribution
It introduces an exact analytical approach to determine critical exponents for the spin quantum Hall transition via supersymmetric mapping.
Findings
Exact critical exponents match numerical results
Mapping to percolation provides new analytical insights
Supersymmetry approach simplifies complex disordered systems
Abstract
We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the two-dimensional percolation problem. The anisotropic limit is an sl(2|1) supersymmetric spin chain. The mapping gives exact values for critical exponents associated with disorder-averages of several observables in good agreement with recent numerical results.
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