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The time-dependent density-matrix theory (TDDM) where theBogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices istruncated by approximating a three-body density matrix with one-body andtwo-body density matrices is applied to the Lipkin model. It is shown that inthe large $N$ limit the ground state in TDDM approaches the exact solution.Various truncation schemes for the three-body density matrix are also testedfor an extended three-level Lipkin model.

Truncation scheme of time-dependent density-matrix approach III