Theoretical Analysis of Two Reconstruction Schemes of Reduced Density Matrices

The effectiveness of the approach for systematical reconstruction of higher order reduced density matrices with lower order ones, which was developed by Chen (Science in China B, 2006, 49: 402), was compared theoretically with that of Mazziotti's method through Harris model, by omitting the cumulant terms 3ΔM, 4ΔM in the latter method and the normal product terms 3Δ, 4Δ in the former method, it was found that the errors from both approaches were comparable. As a better approximation, if only fourth-order terms 4ΔM and 4Δ in both methods are neglected whereas the third-order terms 3ΔM and 3Δ are computed from their cor-responding fourth-order terms 4ΔM and 4Δ, respectively, through contractions, the results calculated with Chen's approach not only have the correct signs but also are very close to the exact normal products 3Δ whereas some of the results calculated with Mazziotti's method do not even have the correct signs with respect to the exact cumulants 3ΔM.