Berlin 2005 – scientific programme

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DY: Dynamik und Statistische Physik

DY 25: Symposium Renormalization and Scaling (SYRS) – Contributed Talks II

DY 25.3: Talk

Saturday, March 5, 2005, 16:30–16:45, TU H3010

Limits of real space renormalization group studies of network models for the quantum Hall effect — •Achim Manze and Bodo Huckestein — Theoretische Physik III, Ruhr-Universität Bochum, Bochum, Germany

We consider a models of Integer Quantum Hall systems with two Landau levels where each node represents a 4 × 4 scattering matrix and the bonds correspond to propagation along directed links subject to random Landau level mixing (U(2)-disorder). Restriction to a fractal structure allows for the implementation of a real-space renormalization (RSR). For the single channel model this model has been employed very successfully for the calculation of , e.g., critical conductance distributions, critical exponent of the localization length, and energy level statistics.

Applying the RSR procedure to the two-channel model, we find only two stable phases corresponding to Hall conductivities of ν=0 and ν=2 (in units of e²/h), respectively, even in the limit of weak Landau level mixing. The absence of a stable localized phase with Hall conductivity ν=1 appears to be a feature of the RSR procedure. Comparison of the results of the RSR with exact calculations for small, square systems and weak mixing shows a tendency towards localization with increasing system size for the square systems while the RSR yields delocalization at ν=1.

As the RSR can also be interpreted as a numerically exact treatment of a hierarchical lattice, this study shows that the phase diagrams of a two-channel quantum Hall system on a hierarchical and a square lattice differ in topology, in contrast to the case of the one-channel model.