On the theory of plateau-plateau transitions in Quantum Hall Effect

Abstract

The Lagrangian (action) formulation of the Chalker-Coddington network model for plateau-plateau transitions in quantum Hall effect is presented based on a model of fermions hopping on Manhattan Lattice ($ML$). The dimensionless Landauer resistance is considered and its average is calculated over the random U(1) phases with constant distribution on the circle. The Lagrangian of the resultant model on $ML$ is found and the corresponding $R$-matrix is written down. It appeared, that this model is integrable, rising hope to investigate physics of plateau- plateau transitions by the exact method of powerful Algebraic Bethe Ansatz $(ABA)$.

10 pages, Latex, 3 figures

References in corpus (6)

• The two-dimensional random-bond Ising model, free fermions and the network model
• Multifractality of wavefunctions at the quantum Hall transition revisited
• Network models for localisation problems belonging to the chiral symmetry classes
• Staggered Anisotropy Parameter Modification of the Anisotropic $t-J$ Model
• Generalization of the U_q(gl(N)) algebra and staggered models
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Cited by in corpus (10)

• Random Network Models and Quantum Phase Transitions in Two Dimensions
• Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Localization length index in a Chalker-Coddington model: a numerical study
• An integrable modification of the critical Chalker-Coddington network model
• Network Models: Action formulation
• Grassmann-Gaussian integrals and generalized star products
• A matrix model for strings beyond the c=1 barrier: the spin-s Heisenberg model on random surfaces
• The XXZ Heisenberg model on random surfaces
• Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics