Dresden 2003 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 50: Quantum chaos I
DY 50.4: Hauptvortrag
Freitag, 28. März 2003, 11:00–11:30, G\"OR/226
Real-space renormalization, percolation and statistics at the quantum Hall transition — •Rudolf A. Römer — Department of Physics, University of Warwick, Coventry CV4 7AL, UK
We review recent applications of the real-space renormalization group (RG) approach to the integer quantum Hall (QH) transition [1,2]. The RG approach, applied to the Chalker-Coddington network model, reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, Pc(G), with very high accuracy [1]. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent, νG=2.39±0.01, that agrees with most accurate large-size lattice simulations. Analyzing the evolution of the distribution of phases of the transmission coefficients upon a step of the RG transformation, we obtain information about the energy level statistics (ELS) [2]. From the fixed point of the RG transformation we extract a critical ELS. Away from the transition the ELS crosses over towards a Poisson distribution. Studying the scaling behavior of the LSD around the QH transition, we extract the critical exponent νELS=2.37±0.02. We then incorporate macroscopic inhomogeneities, modeled by a smooth random potential with a correlator which falls off with distance as a power law, r−α [1]. Similar to classical percolation, we observe an enhancement of ν with decreasing α.
[1] P. Cain, R. A. Römer, M. Schreiber, and M. E. Raikh, Phys. Rev. B 64, 235326-9 (2001).
[2] P. Cain, R. A. Römer, and M. E. Raikh, ArXiv: cond-mat/0209356.