Dresden 2003 – scientific programme
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HL: Halbleiterphysik
HL 49: Poster II
HL 49.5: Poster
Thursday, March 27, 2003, 16:30–19:00, HSZ/P2
Renormalization group approach to energy level statistics at the integer quantum Hall transition — •Philipp Cain1, Mikhail E. Raikh2, Rudolf A. Römer3, and Michael Schreiber1 — 1Institut für Physik, Technische Universität, D-09107 Chemnitz — 2Department of Physics, University of Utah, Salt Lake City, UT 84112, U.S.A. — 3Department of Physics, University of Warwick, Coventry CV4 7AL, UK
We extend the real-space renormalization group (RG) approach to the study of the energy level statistics at the integer quantum Hall (QH) transition. To obtain information about the level statistics, we analyze the evolution of the distribution of phases of the amplitude transmission coefficient upon a step of the RG transformation. From the fixed point of this transformation we extract a critical level spacing distribution (LSD) which is somewhat different from earlier large-scale simulations. We find that away from the transition the LSD crosses over towards a Poisson distribution. Studying the scaling behavior of the LSD around the QH transition, we extract the critical exponent ν=2.37±0.02 very close to the value established in the literature. This provides additional evidence for the surprising fact that a small RG unit, containing only five nodes, accurately captures most of the correlations responsible for the localization-delocalization transition at the QH transition.
[1] P. Cain, R. A. Römer, and M. E. Raikh, ArXiv: cond-mat/0209356.