2005/01/11 by Philipp Cain, Rudolf A. Roemer
Physics and Astronomy · #cond-mat.mes-hall
paper · pdf · doi:10.1142/s0217979205029742
published as Int. J. Mod. Phys. B 19, 2085-2119 (2005) · 35 pages, 14 figures, submitted to Int. J. Mod. Phys. B
arxiv created 2005/01/11 · arxiv updated 2009/12/01
We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy. The RG flow of P(G) yields a value of the critical exponent nu that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as RL and RH is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD) which is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with nu=2.37± 0.02. Away from the transition it changes towards the Poisson distribution. We next investigate the plateau-to-insulator transition. For a fully quantum coherent situation, we find a quantized Hall insulator with RH ~ h/e2 up to RL ~ 20 h/e2 when interpreting the results in terms of the most probable value of the distribution P(RH). Upon further increasing RL, the Hall insulator with diverging RH ~ RLkappa is seen. This crossover depends on the precise nature of the averaging of P(RL) and P(RH). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition modeled by a power law correlation in the random potential. Similar to the classical percolation, we observe an enhancement of nu with decreasing correlation range. These results exemplify the surprising fact that a small RG unit, containing five nodes, accurately captures most of the correlations responsible for the QH transition.