  We present the results of an exact diagonalization study of the spin-1/2
Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore
lattice, also known as the square lattice with crossings or the checkerboard
lattice. Examining the low energy spectra for systems of up to 24 spins, we
find that all clusters studied have non-degenerate ground states with total
spin zero, and big energy gaps to states with higher total spin. We also find a
large number of non-magnetic excitations at energies within this spin gap.
Spin-spin and spin-Peierls correlation functions appear to be short-ranged, and
we suggest that the ground state is a spin liquid.
