论文标题
差异降低密度矩阵理论的挑战：总角动量约束
Challenges for variational reduced-density-matrix theory: Total angular momentum constraints
论文作者
论文摘要
变异的两电子降低密度矩阵（V2RDM）方法被推广用于描述总角动量（$ j $）和总角动量的投影（$ M_ {J} $）在非质化汉密尔顿（Hamiltonians）所描述的原子系统中，并且该方法表明该方法表明了严重的Deficiencies。 Under ensemble $N$-representability constraints, v2RDM theory fails to retain the appropriate degeneracies among various $J$ states for fixed spin ($S$) and orbital angular momentum ($L$), and, for fixed $L$, $S$, and $J$, the manifold of $M_{J}$ states are not necessarily degenerate.此外，对于两个电子降低密度矩阵的系统，可以观察到很大的能量误差。在这种情况下，错误源于纯状态$ n $证明性条件的违规情况。不幸的是，这种违规似乎并不是V2RDM理论能量可靠性的良好指标。确定了几个状态的能源错误接近零，但纯净状态明显违反了。
The variational two-electron reduced density matrix (v2RDM) method is generalized for the description of total angular momentum ($J$) and projection of total angular momentum ($M_{J}$) states in atomic systems described by non-relativistic Hamiltonians, and it is shown that the approach exhibits serious deficiencies. Under ensemble $N$-representability constraints, v2RDM theory fails to retain the appropriate degeneracies among various $J$ states for fixed spin ($S$) and orbital angular momentum ($L$), and, for fixed $L$, $S$, and $J$, the manifold of $M_{J}$ states are not necessarily degenerate. Moreover, a substantial energy error is observed for a system for which the two-electron reduced density matrix is exactly ensemble $N$-representable; in this case, the error stems from violations in pure-state $N$-representability conditions. Unfortunately, such violations do not appear to be good indicators of the reliability of energies from v2RDM theory in general. Several states are identified for which energy errors are near zero and yet pure-state conditions are clearly violated.
