Localization Properties of the Chalker-Coddington Model

Abstract

The Chalker Coddington quantum network percolation model is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We study the model restricted to a cylinder of perimeter 2M. We prove firstly that the Lyapunov exponents are simple and in particular that the localization length is finite; secondly that this implies spectral localization. Thirdly we prove a Thouless formula and compute the mean Lyapunov exponent which is independent of M.

29 pages, 1 figure. New section added in which simplicity of the Lyapunov spectrum and finiteness of the localization length are proven. To appear in Annales Henri Poincare

References in corpus (1)

• Hölder continuity of the IDS for matrix-valued Anderson models

Cited by in corpus (8)

• Random Time-Dependent Quantum Walks
• Spectral Stability of Unitary Network Models
• Dynamical Localization of the Chalker-Coddington Model far from Transition
• Correlated Markov Quantum Walks
• Thermalization of Fermionic Quantum Walkers
• Spectral Properties of Non-Unitary Band Matrices
• On absolutely continuous spectrum for one-channel unitary operators
• Dynamical Localization and Transport properties of Quantum Walks on the hexagonal lattice