Geminal theory for strongly correlated few-body systems

Markus Reiher

Airi Kawasaki, Osamu Sugino

José Paulo D'Incao

Airi Kawasaki, Osamu Sugino

We analyze wave functions constructed as a sum of product of two-electron functions, or as a polynomial of geminals, to investigate their ability to represent the ground state of a strongly correlated few-body system. The known difficulty associated with variational determination of the total energy is overcome by applying a tensor decomposition method called Waring decomposition. Convergence speed of the total energy is compared for various polynomial types. The result provides information bridging between geminal product wave functions and the full-CI in the strongly correlated regime, thereby enriching knowledge on the hierarchy of molecular orbital theories of electron pairs.

José M. Arias, María Isabel Gallardo, Manuel Lozano

Airi Kawasaki, Osamu Sugino

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-configuration interaction 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.