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Pure scaling operators at the integer quantum Hall plateau transition.

R Bondesan1, D Wieczorek1, M R Zirnbauer1

  • 1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany.

Physical Review Letters
|May 27, 2014
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Summary
This summary is machine-generated.

Critical scattering states in the integer quantum Hall effect exhibit multifractal statistics. Their wave function moments follow power-law decays, consistent with conformal field theory predictions for quantum critical phenomena.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Hall Effect
  • Statistical Mechanics

Background:

  • Stationary wave functions at the integer quantum Hall effect plateau transitions display multifractal statistics.
  • The Chalker-Coddington network model is a key theoretical framework for studying quantum Hall transitions.

Purpose of the Study:

  • To investigate the multifractal behavior of scattering states in the Chalker-Coddington network model.
  • To explore the connection between critical scattering states and conformal field theory (CFT).

Main Methods:

  • Analysis of wave amplitude moments for critical scattering states.
  • Numerical simulations employing finite-size scaling.
  • Verification of CFT predictions for correlation functions.

Main Results:

  • Moments of critical scattering state wave amplitudes exhibit power-law decay with distance.
  • Numerical results support the proposal that these moments are CFT correlation functions.
  • A three-point function prediction from CFT was successfully verified.

Conclusions:

  • Scattering states at quantum Hall transitions share critical behavior with multifractal wave functions.
  • The findings provide numerical evidence for an underlying CFT governing these critical states.
  • This work bridges the gap between network models and CFT in the context of quantum criticality.