  The Gutzwiller approximate solution to the Gutzwiller wavefunction yields
exact results for the Gutzwiller wavefunction in the infinite dimensional
limit. Implicit in the Gutzwiller approximation is an approximate local form of
the fermion exchange hole. This approximate form is the same for all dimensions
but is incorrect except in infinite dimensions. We implement the correct form
for the exchange hole into the Gutzwiller approximation. We perform
calculations on the one-dimensional Hubbard model at half-filling. They
indicate that the implementation of the exchange hole already brings the
Gutzwiller approximation into very close quantitative agreement with the
results of the full Gutzwiller wavefunction. Metallicity as well as
anti-ferromagnetism are recovered.
