Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker{endash}Coddington model
- Institut fuer Theoretische Physik, Universitaet zu Koeln (Germany)
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{close_quote}s {sigma} 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{close_quote}s nonlinear {sigma} model with couplings {sigma}{sub xx}=N/4 and {sigma}{sub xy}=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{endash}Baxter integrable vertex model are briefly discussed. {copyright} {ital 1997 American Institute of Physics.}
- OSTI ID:
- 527843
- Journal Information:
- Journal of Mathematical Physics, Vol. 38, Issue 4; Other Information: PBD: Apr 1997
- Country of Publication:
- United States
- Language:
- English
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