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
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.
© SIF, Springer-Verlag Berlin Heidelberg, 2010