  We study the localization transition in the integer quantum Hall effect as
described by the network model of quantum percolation. Starting from a path
integral representation of transport Green's functions for the network model,
which employs both complex (bosonic) and Grassman (fermionic) fields, we map
the problem of localization to the problem of diagonalizing a one-dimensional
non-Hermitian Hamiltonian of interacting bosons and fermions. An exact solution
is obtained in a restricted subspace of the Hilbert space which preserves
boson-fermion supersymmetry. The physically relevant regime is investigated
using the density matrix renormalization group (DMRG) method, and critical
behavior is found at the plateau transition.
