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The Gutzwiller approximate solution to the Gutzwiller wavefunction yieldsexact results for the Gutzwiller wavefunction in the infinite dimensionallimit. Implicit in the Gutzwiller approximation is an approximate local form ofthe fermion exchange hole. This approximate form is the same for all dimensionsbut is incorrect except in infinite dimensions. We implement the correct formfor the exchange hole into the Gutzwiller approximation. We performcalculations on the one-dimensional Hubbard model at half-filling. Theyindicate that the implementation of the exchange hole already brings theGutzwiller approximation into very close quantitative agreement with theresults of the full Gutzwiller wavefunction. Metallicity as well asanti-ferromagnetism are recovered.

Effect of the exchange hole on the Gutzwiller approximation in one dimension