# Truncation scheme of time-dependent density-matrix approach III

## TL;DR

This paper applies the time-dependent density-matrix theory to the Lipkin model, demonstrating that in the large N limit it approaches the exact ground state, and explores various truncation schemes for improved accuracy.

## Contribution

It introduces and tests a truncation scheme within TDDM for the Lipkin model, showing improved approximation of the ground state in the large N limit.

## Key findings

- TDDM approaches the exact ground state in the large N limit.
- Different truncation schemes are evaluated for the three-body density matrix.
- The method provides accurate results for the Lipkin model.

## Abstract

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