  We construct entanglement renormalization schemes which provably approximate
the ground states of non-interacting fermion nearest-neighbor hopping
Hamiltonians on the one-dimensional discrete line and the two-dimensional
square lattice. These schemes give hierarchical quantum circuits which build up
the states from unentangled degrees of freedom. The circuits are based on pairs
of discrete wavelet transforms which are approximately related by a
"half-shift": translation by half a unit cell. The presence of the Fermi
surface in the two-dimensional model requires a special kind of circuit
architecture to properly capture the entanglement in the ground state. We show
how the error in the approximation can be controlled without ever performing a
variational optimization.
