Theory of many-body wave functions with correlations

J. L. Ballot, M. Fabre de la Ripelle, Jesús Navarro

Wang Hongwei, Feng Weiguo, MAO HUI-MING +1 more

Based on the Correlated-Basis-Functions (CBF) theory, we have obtained the many-body wave function for the quasi-two-dimensional electron system in Al x Ga 1-x As-GaAs heterojunction. The pair-correlation functions g(R) were calculated, and a new method for the calculation of correlation energy was also presented.

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.

Pina Romaniello

João da Providência, Carl M. Shakin

It is shown that starting with a correlated wave function for nuclear matter of a general form one may make direct correspondence to the conventional diagrammatic theory of Brueckner, Bethe, and Goldstone. In particular, in this work we show that the expression for the three-body-cluster energy is the same as that obtained by Bethe. Also, it is shown that the current approximation which neglects the potential for particle states in the diagrammatic approach corresponds to a neglect of a coupling between the two-body (Bethe-Goldstone) equation and the equation for the three-body-cluster wave function (Bethe-Faddeev). The theory presented here provides a clarification of the relation of the $n$-body-cluster wave functions and the structure of the wave function of the entire system.

Alexandre M. Zagoskin