  We extend the Coleman's antisymmetrized geminal power (AGP) to develop a wave
function theory that can incorporate up to four-body correlation in a region of
strong correlation. To facilitate the variational determination of the wave
function, the total energy is rewritten in terms of the traces of geminals.
This novel trace formula is applied to a simple model system consisting of one
dimensional Hubbard ring with a site of strong correlation. Our scheme
significantly improves the result obtained by the AGP-CI scheme of Uemura et
al. and also achieves more efficient compression of the degrees of freedom of
the wave function. We regard the result as a step toward a first-principles
wave function theory for a strongly correlated point defect or adsorbate
embedded in an AGP-based mean-field medium.
