  A careful study of the supersymmetric version of Pruisken's nonlinear sigma
model for the integer quantum Hall effect is presented. The lattice regularized
model is cast in Hamiltonian form by taking the anisotropic limit and
interpreting the topological density as an alternating sum of Wess-Zumino
terms. It is argued that the relevant large-scale physics of the model is
preserved by projection of the quantum Hamiltonian on its sector of degenerate
strong-coupling ground states. For values of the Hall conductivity close to
e^2/2h (mod e^2/h), where a delocalization transition occurs, this yields the
Hamiltonian of a quantum superspin chain which is closely related to an
anisotropic version of the Chalker-Coddington model. The relation implies that
the ratio of magnetic length over potential correlation length is an irrelevant
parameter at the transition. The superspin chain resembles a 1d isotropic
antiferromagnet with spin 1/2. It has an alternating structure which however
permits an invariance under translation by one site. The conductance
coefficients of a quantum Hall system with N small contacts translate into
N-superspin correlation functions which are governed by conformal invariance.
The superspin formalism provides a framework for studying the crossover from
classical to quantum percolation. It does not however encompass the
frequency-dependent correlations of wave amplitudes at criticality.
