Models for the integer quantum Hall effect: the network model, the Dirac equation, and a tight-binding Hamiltonian

Abstract

We consider models for the plateau transition in the integer quantum Hall effect. Starting from the network model, we construct a mapping to the Dirac Hamiltonian in two dimensions. In the general case, the Dirac Hamiltonian has randomness in the mass, the scalar potential, and the vector potential. Separately, we show that the network model can also be associated with a nearest neighbour, tight-binding Hamiltonian.

Revtex, 15 pages, 7 figures; submitted to Phys. Rev. B

References in corpus (8)

• Scaling Theory of the Integer Quantum Hall Effect
• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus
• Logarithmic Operators and Hidden Continuous Symmetry in Critical Disordered Models
• The Liouville Theory as a Model for Prelocalized States in Disordered Conductors
• Universal Multifractality in Quantum Hall Systems with Long-Range Disorder Potential
• Transitions Between Hall Plateaus and the Dimerization Transition of a Hubbard Chain
• On The Random Vector Potential Model In Two Dimensions
• Two-Dimensional Electrons in a Strong Magnetic Field with Disorder: Divergence of the Localization Length

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