Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach
arXiv:cond-mat/9701010 · doi:10.1103/PhysRevB.56.1422
Abstract
We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.
17 pages, RevTex, 7 figures
References in corpus (1)
Cited by in corpus (33)
- Random Network Models and Quantum Phase Transitions in Two Dimensions
- Critical exponent for the quantum Hall transition
- Quantum Hall fluctuations and evidence for charging in the quantum Hall effect
- Point-Contact Conductances at the Quantum Hall Transition
- Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
- Scaling Properties of Conductance at Integer Quantum Hall Plateau Transitions
- Localization in the quantum Hall regime
- A metallic phase in quantum Hall systems
- Criticality in amorphous topological matter -- beyond the universal scaling paradigm
- A unifying model for several two-dimensional phase transitions
- Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
- Renormalization group approach to energy level statistics at the integer quantum Hall transition
- Random network models with variable disorder of geometry
- Near-Perfect Correlation of the Resistance Components of Mesoscopic Samples at the Quantum Hall Regime
- Quantum Breakdown of the Quantized Hall Insulator
- Quantum Hall Criticality, Superconductor-Insulator Transition and Quantum Percolation
- Quantum site percolation on triangular lattice and the integer quantum Hall effect
- Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar
- Localization Length Exponent, Critical Conductance Distribution and Multifractality in Hierarchical Network Models for the Quantum Hall Effect
- Nonchiral Edge States at the Chiral Metal Insulator Transition in Disordered Quantum Hall Wires
- Weakly chiral networks and 2D delocalized states in a weak magnetic field
- Localization in non-chiral network models for two-dimensional disordered wave mechanical systems
- Fluctuating Hall resistance defeats the quantized Hall insulator
- Real-space renormalization-group approach to the integer quantum Hall effect
- Possible existence of a band of extended states induced by inter-Landau-band mixing in quantum Hall system
- Conductance distribution between Hall plateaus
- Interplay of Short-Range Interactions and Quantum Interference Near the Integer Quantum Hall Transition
- Localization properties of random-mass Dirac fermions from real-space renormalization group
- Two-terminal conductance fluctuations in the integer quantum Hall regime
- Extended critical phase in quasiperiodic quantum Hall systems
- Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
- Killing the Hofstadter butterfly, one bond at a time
- Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics