  We show that the localization transition in the integer quantum Hall effect
as described by the Chalker-Coddington network model is quantum critical. We
first map the anisotropic network model to the problem of diagonalizing a
one-dimensional non-Hermitian non-compact supersymmetric lattice Hamiltonian of
interacting bosons and fermions. Its behavior is investigated numerically using
the density matrix renormalization group method, and critical behavior is found
at the plateau transition. This result is confirmed by an exact, analytic,
generalization of the Lieb-Schultz-Mattis theorem.
