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

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 $(ABA)$.