Eur. Phys. J. A (2010) 45: 257-266
https://doi.org/10.1140/epja/i2010-11002-5

Regular Article - Theoretical Physics

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

¹ Kyorin University School of Medicine, Mitaka, Tokyo, 181-8611, Japan
² Institut de Physique Nucléaire, IN2P3-CNRS, Université Paris-Sud, F-91406, Orsay Cedex, France

^* e-mail: tohyama@ks.kyorin-u.ac.jp

Received: 28 February 2010
Revised: 7 June 2010
Accepted: 11 June 2010
Published online: 8 July 2010

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 the 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.