Density-matrix formalism with three-body ground-state correlations

TL;DR

This paper develops a density-matrix formalism incorporating three-body ground-state correlations, significantly improving the description of the Lipkin model's ground and excited states beyond two-body truncations.

Contribution

The paper introduces a density-matrix approach that includes three-body correlations, addressing limitations of two-body truncation schemes in the Lipkin model.

Findings

Three-body correlations improve ground state accuracy

Inclusion of three-body correlations satisfies stability conditions

Standard Lipkin model lacks mean-field effects, highlighting correlation importance

Abstract

A density-matrix formalism which includes the effects of three-body ground- state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that inclusion of the three-body correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition.