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

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


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.


Saddle Point System Size Conductance Distribution Integer Quantum Random Matrix Ensemble 
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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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