Martin R. Zirnbauer

---

The scaling behavior near the transition between plateaus of the
Integer Quantum Hall Effect (IQHE) has traditionally been interpreted
on the basis of a two-parameter renormalization group
ow conjectured from Pruisken's non-linear sigma model. Yet, the conformal
Field theory (CFT) describing the critical point remained elusive, and
only fragments of a quantitative analytical understanding existed up
to now. Here we carry out a detailed study of the current-current
correlation function for the conductivity tensor, initially in the Chalker-
Coddington network model for the IQHE plateau transition and then
in its exact reformulation as a supersymmetric vertex model. We take
the continuum limit of the non-local conductivity response function
at criticality and thus identify a non-Abelian current algebra at level
n = 4. By proposing precise lattice expressions for the CFT primary
Fields we predict the multifractal scaling exponents of critical wave
intensities to be Δ_q = q(1-q)/4.

---

Universität zu Köln
ETP 003
Contact: not specified