  The supersymmetric reformulation of physical observables in the
Chalker-Coddington model (CC) for the plateau transition in the integer quantum
Hall effect leads to a reformulation of its critical properties in terms of a
2D non-compact loop model or a 1D non-compact $gl(2|2)$ spin chain. Following a
proposal by Ikhlef, Fendley and Cardy, we define and study a series of
truncations of these loop models and spin chains, involving a finite and
growing number of degrees of freedom per site. The case of the first truncation
is solved analytically using the Bethe-ansatz. It is shown to exhibit many of
the qualitative features expected for the untruncated theory, including a
quadratic spectrum of exponents with a continuous component, and a normalizable
ground state below that continuum. Quantitative properties are however at odds
with the results of simulations on the CC model. Higher truncations are studied
only numerically. While their properties are found to get closer to those of
the CC model, it is not clear whether this is a genuine effect, or the result
of strong finite-size corrections.
