Four-body correlation embedded in antisymmetrized geminal power wave function

TL;DR

This paper introduces an extended wave function theory based on antisymmetrized geminal power that incorporates up to four-body correlations, improving accuracy and efficiency for strongly correlated systems.

Contribution

It develops a novel trace formula for variational energy calculation, enabling inclusion of four-body correlations in AGP wave functions.

Findings

Significantly improves results over previous AGP-CI methods.

Achieves more efficient wave function compression.

Demonstrates effectiveness on a Hubbard ring model.

Abstract

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.