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Real-Space Renormalization and Energy-Level Statistics at the Quantum Hall Transition

  • Rudolf A. Römer
  • Philipp Cain
Chapter
Part of the Advances in Solid State Physics book series (ASSP, volume 43)

Abstract

We review recent applications of the real-space renormalization group (RG) approach to the integer quantum Hall (QH) transition. 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. 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). 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 ELS around the QH transition, we extract the critical exponent νELS=2.37±0.02.

Keywords

Saddle Point System Size Conductance Distribution Integer Quantum Random Matrix Ensemble 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • Rudolf A. Römer
    • 1
  • Philipp Cain
    • 2
  1. 1.Department of Physics and Centre for Scientific ComputingUniversity of WarwickCoventryUnited Kingdom
  2. 2.Institut für PhysikTechnische Universität ChemnitzChemnitzGermany

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