Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model

Source abstract

An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N=1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using a recently discovered equality of integrals, the network model is transformed into a lattice field theory defined over Efetov’s σ model space with unitary symmetry. The transformation is exact for all N, no saddle-point approximation is made, and no massive modes have to be eliminated. The naive continuum limit of the lattice theory is shown to be a supersymmetric version of Pruisken’s nonlinear σ model with couplings σxx=N/4 and σxy=N/2 at the symmetric point. It follows that the model for N=2, which describes a spin degenerate Landau level and the random flux problem, is noncritical. On the basis of symmetry considerations and inspection of the Hamiltonian limit, a modified network model is formulated, which still lies in the quantum Hall universality class. The prospects for deformation to a Yang–Baxter integrable vertex model are briefly discussed.